I was using a compressor plugged into an exterior 15 amp circuit when it stopped working. The outlet is still hot because a smaller power tool works when plugged into the same outlet. A table saw that had been working on the same circuit no longer works as well but the outlets are still hot. These outlets are down stream from a GFCI outlet that is not tripped and trips when tested. Thoughts?
You should check if these outlets are attached to the wiring via back stab connections.
Back stab connections can show intermittent connection that could show up when the current demand of the larger appliance is loading the outlet.
If you have back stab connections the recommended course of action is to remove the outlet and replace with a quality one that uses the screws on the side to secure the wires, either by bending the wire the correct direction under the screw head or using the type where the screw tightens a wire clamp behind the screw head. Try to avoid the cheapest outlets that come of 0.49USD in packs of 10 and get one that costs a few USD and is labeled as a better quality unit.