Well, I still don't totally understand it, but I did fix it. So, this device is a remote-controlled signal multiplexer used in nuclear research experiments, so you can bring up signals on a remote scope, while the ion beam is blasting the vault and nobody can be inside.
It runs in a NIM bin that provides regulated voltages, including +6 V. So, I used an L4941 low dropout 5V regulator to power the Beagle Board. This worked fine for a couple years. Some of the units did not heat sink the regulator, but it only got mildly warm, so I **thought** that should be fine. Now, a couple units would crash after running for a couple minutes.
The fix was to bolt the regulator to the case. So, I don;t know if this means that over time the regulators started sagging due to temperature, or the Beagle got more sensitive, or what.
But, the fix seems to be quite solid.
Well, always learning something new...
Jon