The most common cause of this problem is that the clutch *is* slipping when the compressor is cycled on. It's because the clutch gap is out of specification - it gets wider as the friction materials on the clutch wear. It's easily checked with a set of feeler gauges. Should be 0.50mm, plus or minus 0.15mm. When it gets up around 0.80mm you'll start triggering the compressor cutout function of the Klima relay. That's what is happening when the a/c quits until the car is restarted.

Can also be caused by just a little bit of oil on the clutch friction material. Try using a can of spray brake cleaner, or even just simple green. Thoroughly clean and rinse the clutch areas on the compressor. Then give it a shot. It'll definately cutout while still wet, but when dry it may work for you. I know of one person who fought this problem for a long time, and finally fixed it with a 2 dollar can of degreaser.