My own little odd discovery is that while using ONLY Bluetooth all day/all week it never randomly shuts itself off... However, as soon as I fire up the wifi, Bluetooth is a goner. It seems to shut itself off - and its repeatable. I started using the WIFI program that was created to turn the Mogul into a WIFI access point and my Bluetooth just won't stay on. As soon as I shut off the WIFI radio with the switch, I can leave Bluetooth on all day without issue.
Not that it really matters anyway, as soon as I turn on the WIFI radio my headset will no longer connect to the phone, which kind of ruined the whole Mogul as WIFI hotspot novelty for me.