The Firefox find issue has always been a pain and it still isn’t fixed in Firefox 1.07 or the Firefox 1.5 beta 2. However, I’ve found that you can work around this issue if you turn off the “Begin finding when you begin typing” option in the Firefox Advanced Options dialog:
I’ve been running both Firefox 1.07 and Firefox 1.5 beta 2 with this configuration for around a week and haven’t experienced the problem since then. Your mileage may vary though, so let me know if this workaround doesn’t work for you.