I can't seem to find anything on this, anywhere, so far...
I recently bought a 645 AFD and a P25+ back. Everything seemed to work fine, including the mirror lockup. Just last week I was shooting in Utah and I setup my shot, locked the exposure (AEL), locked up the mirror, and... the shutter wouldn't release. I tried both the electronic release and manually pressing the button. A little later, back at the motel room, I tried all three of my lenses and the results were the same (not a lens problem). I also tried variations in turning on the back and camera (first one then the other), removing the batteries and replacing, removing the back and cleaning the contacts, etc. I tried it again the next day and had the same problem. I had to shoot the rest of the trip without using the mirror lockup.
Now that I'm home in Seattle, I thought I'd try it again; it works as it should and the shutter trips! Offhand, the only two essential differences between here where it works, and there where it doesn't is: 1. It was hotter there with temps in the 90s, and 2. I was at altitudes about 6,000 feet.
I'm going to give KEH (where I bought the camera) a call tomorrow to see if they have any advice (and maybe send it in to check it out). But I thought I'd also post this to see if anyone else had had a similar problem and might know of a solution, or might have an idea as to why this would happen.