Good day to all!!

I own a Honda Civic FD bought in 2009. We suddenly noticed that the air conditioning system wasn't functioning properly. It seems that after the compressor automatically turns off when you reach the desired temperature, it won't turn back on when the temperature rises again. You constantly have to turn the aircon switch off then on again multiple times just so the compressor engages again. When I brought it in to the casa, they said it was the AC field coil set which would set me back around 17k.

Sirs, may I ask if the casa did make the right diagnosiss? If so, does anyone here know of reputable shops near manila or Qc to have this repaired since the casa price is a bit high for me. Thanks in advance