Try cleaning out the compressor clutch. Any accumulated oil/grease/grime can cause it to slip and trigger the cutout circuit. A spray can of brake cleaner into the clutch gap is a good start. It's cheap, it's easy, and it's been known to fix cut-out problems.

If you have a set of feeler guages, check the clutch gap. Ideal is 0.50mm. Clutch engagement becomes unreliable when it gets in the range of 0.80 - 0.90mm. It's possible to adjust it be pulling the front clutch plate and removing/swapping different spacers (essentially small, thin washers). A decent a/c shop will have kits of spacers for Nippondenso compressors.

- JimY