There are two types of self-resetting circuit breakers..
ONE will always test for continuity (if that's all you check) even if it's open, the other won't.
The type that always tests good for continunity you have to REMOVE POWER for a period of time (or else remove all he load) then it will (in theory) reset.
I have one on the bench in pieces as I type this.
Here is why, This is a "hold open, self reset when load/short removed" type. it has a heater coil wrapped around the main bi-metal bar. Normally current flows through the bi-metal bar and the heater only has a small trickle (not enough to heat it) but if excess current flows, the breaker OPENS, now the heater is connected ACROSS the terminals so it's getting the full 12 volts, it gets hot enough to burn my fingers (Well I got off it in time) I have at least two of that type in this rig. ONE runs my air conditioner. That one just got replaced it is the one on the bench.
Try disconnecting the battery for like 20 minutes, Then if that don't work, new breakers.
Home is where I park it!