Hi!

Pressure switch contacts look OK, and there's minimal voltage drop
across under load. Wiring looks OK, too.

Good to know. It never hurts to rule out anything particularly obvious. It
also would not hurt to check the wiring connections in the motor--are they
rusty, burned, loose or just bad? If the motor has a built in circuit
breaker, is it good? (A bad one could have burned contacts or start to open
up just enough when the load increases.)

Could a capacitor issue cause the motor to start fine, but not have
enough power when running?

If it's a "run" capacitor, yes. Starting is the hardest time for a motor,
and some of the air compressor motors I've seen have a dedicated start
winding (and cap) to give them a little more "kick" to get going. That
winding won't stand continuous operation, so it's taken out of circuit by a
centrifugal switch when the motor reaches a certain speed.

From that point the motor runs on a different set of windings. Since it
sounds like the motor runs fine up to a point where the load increases, my
money would be on a run capacitor or wiring/current delivery issue. The run
capacitor would serve to give the motor a little more kick when the load
increases against it.

Capacitors for electric motors are usually pretty cheap. I had a furnace fan
motor that would not start reliably and paid $7 and change for a new one. It
made all the difference in the world. They're certainly cheaper than
replacing a burned out motor.

William