"My TV keeps on stopping working?" Is that grammatically correct?

No.

"My TV keeps not working", "My TV works intermittently", or "My TV keeps stopping" would be better grammatically.

No..

My TV only works when it wants to..

My TV is broken and needs repair or I need a new one.

I know not funny huh.. but be careful with any appliance that keeps shutting itself off.. to point out the obvious there is something wrong with you tv. And if its a short in the cord could cause a fire..

If is not correct:

My TV stopped working.

My TV has stopped working.

My TV does not work.

My TV is not always working.

Hope these help.

The point is: Is it working or did it stop working?

You want to be clear of the action of what your tv did or did not do.

"My TV" is the noun phrase subject

"keeps on" is a phrasal verb

"stopping" is a gerund

"working" is a gerund.

Problem is, you can't have 2 gerunds in a row like that (it is like having 2 unrelated nouns in a row).

It is probably enough to say, "My TV keeps on stopping".

However, a more descriptive word than "stopping" could clarify the meaning. For a couple of examples: "My TV keeps on shutting off" or "My TV keeps on flickering off and on"

Not quite. Try one of these:

My TV is broken.

My TV no longer works

My TV works only intermittently.

My TV works intermittently.

Intermittently, in your context, means that sometimes your TV works and sometimes it doesn't.

This is not grammatically correct you would say my tv has stooped working.

"My TV constantly stops working," would be a better, and proper, sentence. Good luck.

No it is not.

My television set continues to malfunction.

No.

One way:

My TV continuously stops working.

NO! My t.v. continues to quit working. This might be better.