Have you service a relay before? I’m not referring to the solid state relay but the common electromechanical relay that is found in Monitor/Tv board. Electromechanical relays have a moving plate with contacts on it, while solid-state relays work similar to transistors and have no moving parts. The contacts in the electromechanical relay are pulled towards the electromagnet while current is flowing it. The contacts are connected to a spring that pulls them back when the current stops flowing. If this contact have problem , it will cause intermittent problem. You can sometimes gently knock on the relay with the handle of the screw driver to see if it has problem or not. Do not knock it too hard otherwise you may think that the relay have problem. In other word, a good working relay may show problem if you hit it too hard.
Assuming the relay have problem, you can use a small saw to saw or peel off the cover. Then you can use a sand paper on the contact point. Sometimes you could see black burnt mark on the contact point. Seal the cover back with super glue once you have done the servicing.