There are always too many rumours about about why cons stop. In CF's case the rumours weren't coming from any agenda in particular; it's just human nature to spread gossip. The Burned Furs had long since stopped being a thing by the time CF came to an end. The main reason for CF's decline was moving CF10 further south and to a less favourable date, and Further Confusion rising to fill its old time slot, and being more geographically convenient.
First, something to explain about the Burned Furs - there were basically three main points to their complaining: They thought that behaviour in the fandom was significantly crossing some kind of threshold. They thought that individual fan's reputations would suffer. They thought the solution to this was to kick people they didn't like out of the fandom. The reason the Burned Furs got any traction and support in the first place - was because a good chunk of the fandom agreed with them on the first point only. The BFs had broken the ice on a subject that fans had been tip-toeing around, and this was seen as an opportunity - not to kick anyone out of the fandom, but to discuss behaviour and the meaning of the fandom in an intelligent manner. This was... back in 1997-1998? Keep in mind that a year before, the fandom's discussion boards on Usenet had fractured into two (alt.fan.furry vs. alt.lifestyle.furry) - and had stopped talking to each other. No message cross-posting allowed.
Instead what we got were constant message board flamewars. The people who wanted to have an intelligent discussion found out it was impossible to do so. The die-hard Burned Furs and those who opposed them on every point would hijack any discussion. That's when the Burned Furs really lost their credibility, especially as its less-restrained members felt increasingly confident to really voice their hatred. Three years of flamewars later (2001), no one wanted to risk discussing furry issues at all, out of fear of being viewed as a troll and troublemaker. But mainly because we were all sick of the in-fighting.
Ok. Now, we jump back to ConFurence. Each year, the con gets bigger, the parties get just a little rowdier, and the rumours along the lines of "OMG did you hear what someone did at the con this year??" get more extreme. CF8 (in early 1997) was when these rumours reached their peak. Most of them were anecdotal. What was new and worrisome about the rumours - was that a lot of the regulars, who certainly enjoyed a good party and at least some uninhibited hijinks - were starting to feel concerned. (This is probably what also helped give the BFs some of their early traction).
Mark Merlino, the con chair, suffered from the same thing that Uncle Kage and Dragoneer get - a group of people constantly bashing them and blaming them for everything, and a group of supporters that always backs them up. But here's the thing: the next year, CF9, that was ConFurence's biggest year. And there were a lot less rumours and complaints. So whatever had happened with all the fandom politics between those two years - The con staff and all the attendees turned things down a slight notch and a good time was had.
Then CF10 happens, it changes the date and moves south, and Further Confusion rises to fill its gap in the San Francisco Bay Area, and Mark and Rod (Mink, in his post above), step down as con chairs. CF11 to CF14 will be run by Darrel Exline. Because of Mark's detractors, a couple of the new furry cons that spring up across the country make a not-so-subtle point to change their con chair occasionally, or cycle their top staff members from year to year.
Now, there is a link between ConFurence and the Burned Furs: When Darrel becomes con chair, he announces that he's a Burned Fur. This is before the BFs had lost their credibility. Darrel is of the "Let's discuss behavior" camp, not the "Purge the fandom" camp. He used to be on CF's security staff; he wants hobbyists and lifestylers alike to enjoy the con - just not to push it any further towards what CF8 was starting to feel like. Unfortunately Darrel's way of posting his views come off as hot-headed and off-putting. Immediately there's a group of Burned Fur-haters who start a hate campaign towards Darrel and CF in general. Darrel doesn't deal with this well politically; he eventually apologizes for his initial BF stance, but by that time it's at least two years too late.
Despite what anyone says about Darrel, he tries to run the con as best he can, only he's not quite cut out for it. ConFurence slowly loses momentum while Further Confusion (and other cons) grow. Finally Darrel calls it quits. If you want to read Darrel's take on the things he did wrong, look no further than his opening essay in the CF14 conbook, archived here.
I don't know what rumours you've heard about the demise of ConFurence, but that's my take on it.
There are always too many rumours about about why cons stop. In CF's case the rumours weren't coming from any agenda in particular; it's just human nature to spread gossip. The Burned Furs had long since stopped being a thing by the time CF came to an end. The main reason for CF's decline was moving CF10 further south and to a less favourable date, and Further Confusion rising to fill its old time slot, and being more geographically convenient.
First, something to explain about the Burned Furs - there were basically three main points to their complaining: They thought that behaviour in the fandom was significantly crossing some kind of threshold. They thought that individual fan's reputations would suffer. They thought the solution to this was to kick people they didn't like out of the fandom. The reason the Burned Furs got any traction and support in the first place - was because a good chunk of the fandom agreed with them on the first point only. The BFs had broken the ice on a subject that fans had been tip-toeing around, and this was seen as an opportunity - not to kick anyone out of the fandom, but to discuss behaviour and the meaning of the fandom in an intelligent manner. This was... back in 1997-1998? Keep in mind that a year before, the fandom's discussion boards on Usenet had fractured into two (alt.fan.furry vs. alt.lifestyle.furry) - and had stopped talking to each other. No message cross-posting allowed.
Instead what we got were constant message board flamewars. The people who wanted to have an intelligent discussion found out it was impossible to do so. The die-hard Burned Furs and those who opposed them on every point would hijack any discussion. That's when the Burned Furs really lost their credibility, especially as its less-restrained members felt increasingly confident to really voice their hatred. Three years of flamewars later (2001), no one wanted to risk discussing furry issues at all, out of fear of being viewed as a troll and troublemaker. But mainly because we were all sick of the in-fighting.
Ok. Now, we jump back to ConFurence. Each year, the con gets bigger, the parties get just a little rowdier, and the rumours along the lines of "OMG did you hear what someone did at the con this year??" get more extreme. CF8 (in early 1997) was when these rumours reached their peak. Most of them were anecdotal. What was new and worrisome about the rumours - was that a lot of the regulars, who certainly enjoyed a good party and at least some uninhibited hijinks - were starting to feel concerned. (This is probably what also helped give the BFs some of their early traction).
Mark Merlino, the con chair, suffered from the same thing that Uncle Kage and Dragoneer get - a group of people constantly bashing them and blaming them for everything, and a group of supporters that always backs them up. But here's the thing: the next year, CF9, that was ConFurence's biggest year. And there were a lot less rumours and complaints. So whatever had happened with all the fandom politics between those two years - The con staff and all the attendees turned things down a slight notch and a good time was had.
Then CF10 happens, it changes the date and moves south, and Further Confusion rises to fill its gap in the San Francisco Bay Area, and Mark and Rod (Mink, in his post above), step down as con chairs. CF11 to CF14 will be run by Darrel Exline. Because of Mark's detractors, a couple of the new furry cons that spring up across the country make a not-so-subtle point to change their con chair occasionally, or cycle their top staff members from year to year.
Now, there is a link between ConFurence and the Burned Furs: When Darrel becomes con chair, he announces that he's a Burned Fur. This is before the BFs had lost their credibility. Darrel is of the "Let's discuss behavior" camp, not the "Purge the fandom" camp. He used to be on CF's security staff; he wants hobbyists and lifestylers alike to enjoy the con - just not to push it any further towards what CF8 was starting to feel like. Unfortunately Darrel's way of posting his views come off as hot-headed and off-putting. Immediately there's a group of Burned Fur-haters who start a hate campaign towards Darrel and CF in general. Darrel doesn't deal with this well politically; he eventually apologizes for his initial BF stance, but by that time it's at least two years too late.
Despite what anyone says about Darrel, he tries to run the con as best he can, only he's not quite cut out for it. ConFurence slowly loses momentum while Further Confusion (and other cons) grow. Finally Darrel calls it quits. If you want to read Darrel's take on the things he did wrong, look no further than his opening essay in the CF14 conbook, archived here.
I don't know what rumours you've heard about the demise of ConFurence, but that's my take on it.