Muffler effect air conditioner?

I may be way off on this but I'm basically running out of answers/options with this. So I have an old car (1996 Honda Accord) and I've had it for a year or so. The only problems with the car is that there is a hole in the muffler that causes it to make a loud noise when turning on and while driving it (not the biggest issue). The issue is is that my air conditioner would be cool for about 15-20 minutes then basically give out and just blow out air. Does anyone know if the hole in the muffler would effect it? If not does anyone know if any way i could fix this? The antifreeze is fine btw, got it checked already. Thanks in advance

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