27" FLAT SCREEN RCA, KEEPS TURNING ON AND OFF BY ITSELF

If the main board have damaged, this kind of fault can occur.

sounds like your power switch is broken. Take the battery out of the remote and see if it still turns on and off. If not its your remote. If it keeps doing that, you may have to get the power button replaced.

Check for bad capacitors in the power supply. Check for voltages. You can get a board at Encompas Parts.,

check the energy saver settings

Most likely, a number of capacitors need to be replaced in the power supply on this set, OR possibly, there is a bad connection on a connection on the snubber capacitor in the power supply, near the SMT transformer--and I have seen this MANY times on westinghouse LCD sets. .

We have a solution to this link that will help

http://www.fixya.com/support/r6019270-refrigerator_freezer_air_conditioner

i would keep it. you will have to replace a few components on the power board but, its not very expensive to do so.

Same with me

For some reason it is overheating and shutting itself off. There is a law that all electronics are supposed to have a point to where it automatically shuts off if it gets too hot from a malfunction or loose connection in the circuit board. It is to protect the consumer. You either need to take it to a tech or get rid of it. Get a new one.