Inside this monitor is a power supply. The power supply converts the AC electricity you have, (120 volts or 220 volts. Depends on what country you're in), to the needed voltage for the monitor.

The power supply is going bad. This is why you can turn it off and back on, and it works for a few minutes.

More than likely it's Electrolytic Capacitors that are going bad, within the power supply itself.
These capacitors break down due to a variety of problems. The largest issue, is that they are cheap components, and have an inherent problem before they were installed.

Capacitor Plague.
Let me explain. A number of years ago a certain individual stole an Electrolytic Capacitor paste formula.

[To simplify the construction of an Electrolytic Capacitor, let me state they are small aluminum 'cans', and have Electrolytic paste inside. (Ones used for computer related capacitors)

For a more detailed explanation of Electrolytic Capacitor construction, I invite you to go to Wikipedia.org, and type -> Electrolytic Capacitor <- in their search bar. Look under the Construction heading]

Unknown to the thief they were given a bogus formula. This formula of Electrolytic paste developed a gas after time. (Hydrogen gas)

This gas expands in the capacitor, breaks a seal, and Electrolytic paste starts oozing out.
For a small amount of paste loss, the capacitor operates in a weakened state.
Such as what you're experiencing.
After so much paste loss, the capacitor fails.

There is more than one capacitor that is used, in that monitor power supply. Some are still good enough to get the monitor to power on, but can't sustain power, so they can't keep the monitor on.

I know this may be way more information than you wanted, or needed, but I thought I would explain exactly what is going on.

Solution? I suggest you replace the monitor. Opening a monitor is VERY dangerous. I Do Not advise trying to fix it.