In my experience the most common cause of this problem is an excessive clutch air gap and/or grease & oil on the clutch. Check the clutch air gap with a common set of feeler guages, such as are used for valve clearance or spark plug gapping. It should be 0.50mm, with a variance of no more than 0.15mm. I find once it reaches 0.8mm the compressor cutout circuit begins to engage.
A simple possible fix is to just degrease the clutch. Get some aerosol brake cleaner (or similar) and spray it into the air gap to thoroughly soak and clean both surfaces. Sometimes this adds enough additional 'stiction' to avoid the compressor cutout circuit.