Sure sounds like a leak is somewhere. Soapy water is good for that.
Are you running an air tank of any sorts? Won't stop the leak, but will stretch out the compressor cycle times. Those short runs every few seconds are tough on a compressor. The initial start up is the highest current pull and highest load. Doing that every few seconds is tough on the compressor. High loads, more heat, short run time, no cooling. Even a small storage tank (size of a soda can?) will help out on the cycle times. To the point of maybe getting a couple of activation cycles before the compressor has to cycle.
Any idea what pressure switch is on the compressor? I've seen lots of different values. The last (real ARB) compressor I got was a 150/175PSI where the identical clone had a 50/80 PSI pressure switch installed. I put 90/120 in both of them to get pressures closer to what I want to use.