Fix didn't work for me
I have the same display going out problem on my 98 Explorer CD/Tape in dash Radio. I've noticed that mine doesn't normally just go out, it dims first and fades away slowly. This doesn't sound like a poor connection but I thought I would try the suggested fix anyway. I have a soldering iron and a lot of experience soldering. I also have a Stereo Microscope which works perfect for looking at small solder joints. My solder joints looked fine but I thought that maybe just disconnecting the connectors and reconnecting them might clean a poor connection, no luck. I took it apart again and resoldered all the display solder joints anyway and I checked every solder joint on the board under the microscope, they all looked good. This time the display didn't work at all! Opps, but then it started working and stayed working for about 5 minutes. It's out again now. So at least for me, this fix didn't work. I think more than likely the problem is in the components not the connections.
I did learn a tip however that I will pass on. I had a very hard time getting my radio out, even with the special tools. Once I finally got it out I looked closely at the little latch to see how it works. The important thing is, you have to push the tool in the right distance, then push them away from each other, and pull. There is a small cut out on the side of the radio where the end of the tool has to go in order to give enough clearance. If you don't push them in far enough the tabs won't clear the catch, if you push them in too far you pass the hole and the tabs won't move. There is only 1/8 inch between not far enough and too far. On my stereo I measured it. The ideal depth to push them in is 1 and 5/16th's Inch. Even at that, I had to use a couple of screw drivers to gently pry the radio face plate out from the dash. The key is, at the right depth the tool (nails should work) you'll be able to push the tools a little further apart from each other because they will be going into the hole.
Hope this helps someone, sorry for the super long post.