I noticed that mine froze when it got down to one bar. It was while my neighbor was borrowing it, and she was afraid she had broken it.
However, I just recharged it and then hit the reset on the back, and it was just fine. Since then, I plug it in while I'm at my desk, or if I plan to use it as a browser for any length of time.
Although, I have found that if I'm browsing a specific site (like the tv listings) I can leave it in Whispernet mode just long enough to allow the page to load, and then I can turn it off and flip between the pages of the site while they are still in memory.