its usually one of two things, thermal shutdown or the HT transformer or other HV section of the monitor going out of limits, if its either then its time to take it to a shop and get an estimate for a repair, try to find a store that will do a free estimate, sometimes its cheaper to buy a new one, sometimes not.
occasionally its something as simple as "dry joints" with the voltages usd in monitors the soldered joints "dry out" and the connection breaks, and you get intermittent problems, a shop just finds them and resolders them. if its that simple a fix and the shop is a fair one, it should be pretty cheap to fix, probably around $50.
however its a case of finding out, thats where the free estimate comes in
don't attempt to do it yourself unless you are familiar with live 24KV chassis and such, monitors are giant capacitors and they hold a potentially lethal charge even after been off, sometimes for weeks. i have a scar to prove it