likely keys include
app.update.mode (would need to look at the code to find what values other than '1' do)
app.update.url (if it's looking the wrong place for an upgrade, it won't find anything to upgrade to. you could even point this at a system you manage so that you get the benefits of auto-updating at the client, but on your schedule)
I would expect that a google search, or a search of the mozilla forums/lists would give you more concrete answers.
Personally, I run the Aurora version everywhere. It tries to update daily and I just ignore the suggestion until I feel like doing so.
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