Falls asleep? Are you talking about Firefox taking a long time to "wake up" if you have it minimized for a long time?

This was filed as a bug some time ago for Mozilla applications in general. I do not recall the bug ID. But it turns out that the problem is that Mozilla apps are "good neighbors" and will yield their space in active memory very quickly when they get minimized, and thus are quickly paged out. Once they are paged out, un-minimizing them takes a long time. Most other Windows apps do not play as nice and actually take steps to prevent them from being paged out into the swapfile when they are minimized, which is why bloatier programs like Photoshop will actually take less time to recover from minimization.

The resolution to the "bug" was the creation of a hidden feature...

In user.js in your profile directory (create user.js if it does not exist), add the following line:
user_pref("config.trim_on_minimize", false);

This was added in FF 0.9. Was broken for a number of the 0.9 releases. And was fixed for 1.0 PR.