Could be a faulty temperature sensor in the transmission.  The PCM will lock
out OD if it thinks the fluid is too hot.  The only way to know for sure is
to hook a DRB3 (dealer scan tool) and see what temperature the sensor is
reporting.  If it's the sensor, replacement is simple enough, but you should
make sure that's what's wrong before just replacing it.  The PCM may also
set an OBD-II code for trans temp., which could be picked up by any generic
OBD-II scan tool.

I take it there's no drivability problems with the transmission?  No
slipping, or anything else that might actually cause the trans fluid to
overheat?  A non-contact IR thermometer pointed at the transmission pan
could verify the fluid temp - if it's under 140°F or so, everything's fine.

Your rig just started this by itself, or did you notice it when you
had initiated the no OD mode and it was "stuck" until you discovered
that off/on/restart would "reset" it?  Have you used the "OD/off/on"
switch very often?  I am guessing that you very likely seldom if ever
use the switch, which leads to my "theory" of the root cause of the
problem:

It almost sounds as if the "OD/off/on" mode switch has slightly
corroded internal contacts, maybe from lack of, or even no use.  I
assume when you first noticed the behavior you cycled the OD switch
several times convincing yourself that it could not be changed via
that approach.  The switch cycling may have been juist enough to
"clean" the internal mechanical contacts slightly allowing it to
regain functionality after you turned it off and restarted it.  Then,
after no further use the corrosion/dirt would again "contaminate" the
contacts after a few days.  If my theory is anywhere close to the
reality, then the problem shouldn't come back if you make a point to
cycle the switch several times each time you operate the vehicle.  The
cycling would keep the corrosion at bay(at least until you could
verify or invalidate my idea) via the friction from the contacts
opening and closing on a regular basis.  Easy enough to verify or
prove the theory wrong....   regards, Joe  (were there any unusual
OBD-II scan codes logged? Perhaps another thing to check to get more
info on the issue, most auto parts store chains will either loan you a
scanner, or do it for you at no cost these days...)