AC problem 2012 honda civic

My vehicle is over 122000 miles and runs great, however,
the ac has started acting up in thr last two weeks. The
vehicle starts out blowing cold air but after 30-40 minutes
of driving, it stops bloeing cold air. The LED lights indicate
the ac is running, but only hot air comes out.  Somrtimes it
will start blowing cold air again, only to stop after 5 minutes
. I took it to PEP Boys, who charged me over 50 dollars
after taxes, to tell me that they ran the ac for about 30
minutes, and injected a dye into the system, and that the
pressures where right and the compressor was loading up
on demand , all this while the vehicle was hooked up to
their machine, the car was running in park. He did mention
that I may hsve a problem with a relay, but that was as far
as he went. Going to take the car to a honda dealership to
have them look at it,  but I don't want to get taken to the
cleaners. Anyone hsve similar issues?  Could sure some
advice right about now. And oh, by the way, I did put AC Pro
in the system, prior to going to PEPBoys and there was no
change, before or since.