1. Run PS or TOP while in offline mode and see if anything is using a ton of CPU time.

2. My second action would be to go offline most and then for next 30 minutes run a cron tab every couple seconds and logs it in a file. Then go through the file looking for anything that is using a ton of CPU time.

3. Add a cron job that runs a scripts every couple minutes that does a "ps" (with whatever options you want) and then look at the log it creates and see what is "eating" the cpu time. In the morning look at it. )

One of those should show you the culprit... Could be something that is trying to activate every so often that is getting in a weird loop when offline. For example; the MicroB browser doesn't clean up all its processes when it is closed.

Nathan