It doesn't update super frequently during the 6-week release cycle. Maybe once a week tops, I think? Hard to be sure, as I restart FF every few days anyway.
Before Aurora there's also http://nightly.mozilla.org/ one update/day. I've run it since shortly after they moved to a six week cycle (I ran Aurora initially) and have never had work loss. Only once in that period have I had to downgrade to Aurora for a day (the nightly build seemed broken, crashed on startup). Overall I'm very happy with getting features and speedups ~18 weeks before general release.
BTW, they must have more or less completely solved the add-ons version compatibility problem that was initially a big pain when they moved to the six week cycle; I haven't noticed any disabled or broken add-ons in a very long time.
A few years back they introduced a "restartless addon" api, so addons didn't use XUL (firefox's internal language) directly. This allows them to be both enabled/disabled while firefox is running, and not need to be rewritten every version. Look for the "restartless" tag on the addon website.
The six-week cycle probably helped as well, since there is less changes between versions; not to mention improved auto-updating.
A small nitpicky correction: XUL is a markup language, but one can certainly write Firefox UI using HTML or XHTML as well. The logic is written JavaScript.
For example, the markup view itself from the Firefox Developer Tools is written in HTML [0] and JS [1]. Other tools like the Network Monitor use XUL.
At the time I was trying Aurora, I kept hitting bugs with FF sync, ended up having to kill my profile a few times.
Also I just happened to occasionally hit plugin/add-on/etc bugs that would require me to kill and downgrade FF, losing ~10 minutes of work and my train of thought. It didn't take long for this to push me to the Beta channel.
Glad to hear Aurora is generally solid for you, though. Maybe I should give it another try.
http://www.mozilla.org/en-US/firefox/beta/
It doesn't update super frequently during the 6-week release cycle. Maybe once a week tops, I think? Hard to be sure, as I restart FF every few days anyway.