Dixie, are you sure that the player is actually pausing, or is it just going quiet and dark for a moment and then continuing to play?

The difference is that if it's pausing there will actually be a pause symbol on the screen. If it's going dark, it might be have a battery icon appear on the screen when it lights up again.

So. If it's just going dark and not actually pausing, I'll bet it's a wiring problem on the harness area behind the sled, such as this problem. It could also be something related to the wiring of your installation, such as having used substandard methods to join wires like crimps or twists instead of proper solder and shrink tubing.

If it's genuinely pausing, do what Rob said and check that the fascia isn't binding against the button. Also check to see that the player isn't getting any stray IR or stalk signals.