I'm sure this happens to everybody exactly once. After the first time, nobody wants to do that again. The trick is that unless there's any activity, the browser session times out after (I think) 20 minutes and if you take longer than that to compose a mail, then you're out of luck.
Solutions include the notification popup, or copying the text before send, or doing some action every now and then, even if it's just an address lookup or anything else to keep the browser session alive.
Yes, it's a pain. I'd guess that this isn't about the Squirrelmail product itself but an issue with web interfaces in general, so I wouldn't blame it on the squirrel - even though it could be smart enough to keep the session alive.
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