My wife's cousin keeps losing power to her bathroom lights and fan. It will be out for a week or so, then come back on for a day to a week, then go back out. I went over and checked the line at the switch, the lights, and the fan. The readings were good (120v-124v) without any bulbs in (she had removed them before I came over). Since I had a good reading in the bathroom, I checked the breaker. The breaker is a 2-pole 15 amp WR and had a good reading as well (123v), but one of the wires was broken and away from the breaker. I reconnected it and retested, everything was checking out. Now, for the weird part that is beyond my basic comprehension. After fixing the breaker, I checked the power in the bathroom and it was still reading fine, but when I put a light bulb back in either of the two light fixtures, it drops to 4v, but does not trip the breaker. When I unscrew the bulb, the power goes back up to 120ish volts. I changed out the breaker and retested. 123v without a light bulb, yet still drops to 4v once a light bulb is plugged in. What can be causing this?
To me this sounds like a bad connection. My first look is for backstabs prior to the switch or at the switch, it can also be a broken wire sometimes a Knick on the wire when striped the wire can break over time, and last a wire not fully in a wire nut. All of these can show full voltage without a load but once a load (the light) is added it opens. I see this most often with backstabs the push in wire connections , I have found a few broken wires and a few more loose wire nuts over the years but most often a bad backstab.
Although I have found this problem hundreds of times on outlets I have found it a few dozen times fed from an outlet on a lighting circuit, Usually lighting circuits are not as heavily loaded but in a daisy chain feed the bad connection is usually close to the switch a outlet that feeds the switch within a few feet. Or the switch itself.
You mentioned a double pole breaker so it might be a multi wire branch circuit, but since both hot to ground and hot to neutral voltage are good I would be looking for a bad hot , black or red wire.