After you shut down for a few minutes and on restart when the a/c works again, does it work on idle for a while ? When the a/c stops blowing cold air, do you see the compressor cut off ? I am trying to understand whether it is mismatch in the engine and the compressor RPM that is causing the compressor to shut off and therefore causing a loss of cooling OR is it the engine temperature OR high compressor outlet pressure (possibly because your aux fan may not be working) that is causing the compressor to shut off.

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Saumil S. Patel