Hello,
If I understand correctly, RUT240 acts as a client to some other wireless access point?
It would be interesting to know what happens after RUT disconnects from WiFi, but before reboots.
I would like you to attach a troubleshoot file to your question. Please, replicate the issue, by disconnecting from the WiFi, then wait some time till device becomes unstable, then access router's WebUI, go to System -> Administration -> Troubleshoot section and download troubleshoot file from there.
If that does not work out, in the same System -> Administration -> Troubleshoot section switch Save log in option to Flash memory, and generate troubleshoot file after one of the unintended device reboots. Be aware that this will increase flash wear, thus should be disabled after generating the file.
The logs in the file might provide more insight into possible cause.
Best regards