It will help in your troubleshooting to determine if when you put a fresh fuse in and turn on the AC does the compressor clutch engage before the fuse blows again?

See if that's happening.

There's really only a few things that would cause that fuse to fry.

• A damaged positive wire to the compressor clutch that's intermittently shorting to ground. Inspect the wiring from the compressor clutch back to the fuse box.                                                                                                   
• A damaged AC compressor clutch relay. Pull out the relay and inspect the sockets it plugs into in the fuse box for heat damage (melting). Maybe replace the relay just to be sure (they're cheap enough). Also inspect the sockets in the fuse box where that 10amp fuse plugs in for the same thing.                               
• The AC compressor clutch is shorting out. Check the AC clutch coil's resistance with a multimeter.                                                                       
• The AC Clutch diode is fried. The diode prevents the voltage spike from backflowing into the relay and that 10 amp fuse which happens every time the magnetic field in the compressor clutch collapses as the relay is opening and power is cut to the compressor clutch.  Check the diode with a multimeter. (it looks like yours is in that harness so if you can't see it you should be able to feel it in there)

You can see in the diagram how the diode is parallel wired with the AC clutch coil in the circuit.

Here's a couple of helpful videos. The 1st shows how to measure the resistance in the AC Clutch coil.

The 2nd shows how to test a diode. 

https://www.youtube.com/watch?v=dEF7DmcCCrY

https://www.youtube.com/watch?v=qSDRsz5-t7I

If you need a multimeter, on the top right corner of this page click on tools, then Diagnostic tools. You'll see a nifty Neoteck Auto Ranging Digital Multimeter for around $25 which is all you need to do these tests to figure out why your 10amp fuse keeps frying