CRT Connection Help; Loss of Clarity after 5+ minutes

If this is the wrong place/there's a better place to post this, please let me know.

The problem I've been having is with an old Sony CRT television that's hooked up to a cable box. Recently, I hooked up a Wii to the CRT using composite video cables, and the image stops being clear after about 5 minutes of use. The colors will fade and the picture will become overwhelmed by static to the point of no longer being visible. If I play with the video connection a bit, the picture will eventually return back to normal, but then after another 5 minutes or so will repeat the process.
Now, I'm almost completely sure this is a problem with the connection itself/the composite input jacks on the CRT. It's pretty clear that this is the case in my opinion because I have a cable box hooked up to it using those screw in cables (RF video? VHR? something like that but that's not really important I think), and when I watch cable on it never has any problems whatsoever. Therefore, it can't be the display, correct? It has to be some sort of issue with the composite jacks. I tested the jacks with other cords and other devices that worked on other TV's and encountered the same issue.
Could the jacks or the connection somehow be corroded or something? How would I fix this?

Edit: If you're wondering why I'm trying to use a CRT so badly, it's because the input lag is the lowest--I'm trying to play competitive smash on it