Can you tell us a bit more detail about the situation? There could be any number of things causing the problem. Here's a few questions that occur to me:
1. What Mac model and monitor model are involved? Include the Mac's specs.
2. What exactly happens when the monitor cuts out (all black, weird colors, etc)?
3. What troubleshooting steps have you tried and what were the results? Example,tried different cable, connecting the monitor to a different computer, connecting the computer to a different monitor.