Sounds like a refrigerant gas issue. Put a set of gauges on it and start it. Once you confirm it's a gas problem, then start looking for the leak. I suspect you're going to find it's low on gas. I had the same/similar symptom and found that the numbnuts who installed it didn't fully tighten one of the fittings behind the condensing unit. It made for a very slow leak, but once it reached that certain point, I would start getting that high pitched winding up noise followed a few seconds thereafter by the condensing unit cutting off. As soon as the time delay ran its x-amount of seconds, the compressor tried to kick on, and this was just a vicious cycle.
I have finally washed my hands of the local CruisAir dealer and have resorted to doing the work myself now, except for getting the system recharged when necessary, and then, I call someone else and tell them what I want rather than asking them to troubleshoot the system. I'm done with that! My last trouble was found to be a solenoid valve that was punctured from the OUTSIDE. ????? No idea how a valve gets punctured on the tube that is enclosed inside the coil. The local dealer wanted to charge me $300+ for parts I found on my own to be a $30 enclosure tube and an $8 coil. I didn't even need the coil but they thought I'd buy it for whatever amount they were going to charge me. Wrong. I spent $30 on ebay for the part and am fixing it myself. I'm figuring out that knowledge is power! I'm tired of these people thinking I'm stupid.
Anyway...I got sidetracked. LOL Go check the gas pressures. I think that's your problem which is going to mean a leak somewhere.