I see that there are two white wires soldered together that are exposed.
Possible that those are touching something when plugged in?
Wrap with a little bit of electrical tape.
The other idea (may be the most plausible) is that the 1/4" jack is just worn out... It may not be making contact like it should be.
Best to replace.
In the short term you may be able to get in there and push the contacts out so that they push against the plug better. Be careful not to break the contacts... I'm sure SE can get a new jack to you.
Have you tried another cable?
That's another possibility.
I think that's all I have for ideas...