I think 5 & 7 are the socket numbers where the Klima relay plugs in, 15 & 87 are the pin numbers on the Klima relay itself. If memory serves (usually doesn't in my case...) socket 5 is +12v and socket 7 is the compressor coil.

Got a volt/ohm meter? Check the continuity through the compressor coil to ground, both when cold and the a/c is working, and also when hot and it stops working. I'm starting to think the coil is going open when hot.

Of course, these symptoms also fit an excess compressor clutch gap, which you haven't checked yet.

I don't think it's the compressor-engine speed comparator circuit because the compressor never comes back on after a restart. If it cuts out once it'll do it again, but frequently runs for a minute or two first.

To be thorough I'd also check to see if the CC head unit is calling for compressor operation when it cuts out. I forget which pin this is on the Klima socket; it's on the wiring diagram. Should see +12v on this pin when a/c is called. Easy to test by switching between a/c and econ.

- JimY