From experience I can tell you that the FiOS provided routers are rather unreliable. I had no end of trouble with mine, and eventually just had to install a secondary router to get the functionality and reliability I was looking for.
I am relatively sure that the router provides a networked logging option in the advanced settings. You could potentially use that to push the log entries out to your computer, which would give you an idea as to what is happening in the moments that lead up to the crash. It would be easier to just check them in the router's web UI, but it sounds like you lose access to that once the lockup occurs.
In addition, have you checked the log files on the Linux machine right before you lose the connection?
It is worth noting that BackTrack makes a lot of modifications to things like the WiFi drivers to make them compatible with things like Aircrack, so it is entirely possible that some BT-specific driver modification is causing an issue with the network. You might find that you have no problem when running a standard Linux distribution.
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