Check all your ground wire connections before blaming the solenoid. The overdrive is turned on by the PCM computer when it 'completes the ground circuit' of the 12 volts that goes to the Overdrive clutch solenoid.
If the connection to ground is bad from corrosion, loose bolt, oily surfaces, etc then the solenoid may not be able to draw enough current to stay engaged.
If it shuts off, and you can not immediately get it to turn back on, I would check your transmission fluid.
Everytime mine has ever shut off on it's own, it directly corresponded with my transmission fluid getting too hot. One time, the trans temp light came on just a few minutes after my OD shut off. The other time the OD shut off, but the trans temp light did not come on, but I knew I was running very hot (probably just not quite hot enough to set off the trans temp light that time). Once everything cooled down, I was able to turn it on and off again.
I have since installed an auxillary transmission cooler. Now my transmission fluid stays much cooler (I have a guage so I can monitor it). Have never had the OD shut off on it's own since.
mine did it and i ask a friend at dodge to look and my trans was getting to hot so he said it was comming on its a protection thing that the computer makes it do. My trans cooler lines were a cloged up .