on the power board inside the monitor you have a series of capacitors, some of those are going bad.
when voltage is applied thru them, they sort of overload, and turn off the display. you let it cool down for a few seconds/minutes and the capacitors drain... and when you turn it back on, it works for a second and the process repeats
you can replace the capacitors, or the power board, or the monitor. in most cases, the time it takes isn't worth the end result considering how low cost the monitors themselves are.
the capacitors can be purchased for around $5, the power board for around $40 - but it's going to take soldering skills to do it yourself