video trouble

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For the past few months my PS2 plays perfect most of the time, but once in a great while the screen gets a little fuzzy. I play with the A/V cable coming out of the back of the console and the problem goes away. Well I took it to a friend's house, and it did it again, again I touched the cable in the back and the problem went away. Then I took it home, set it back up. No problems then about 20 minutes into playing the screen starts to go fuzzy. I try the normal trick, but this time it doesn't help. Figuring I just need a new cable and no sense in hurting the console I just play it out. About 5 minutes after that the screen becomes unplayable unto the point the TV just shows unusable signal. The RCA jacks on the TV are fine, tested them with another console, and have the same problem on several T.V.'s. So I run up to the store to purcase a new patch cable. I plug it in, do the initial turn on and the picture is as good as new. YAY! Then about 10 minutes into playing the screen goes unplayable and then 'usuable signal' again. Any suggestions?