The simplest solution is to re-route the wires from circuit breakers to switch. I'm not 100% certain, but I think you have 1 A/C that gets power directly from a dedicated circuit breaker. The other A/C circuit breaker powers the switch, where one or the other of the 2 remaining units can be selected.
So I would think the broken unit is the one that gets power directly from its dedicated breaker. You want to move the wires, or splice an extension, so that one unit currently getting power from the switch, instead gets power from the circuit breaker.
This reply is 100% accurate. After digging into the switch, we determined what you said is true. Both the front and middle unit are wired to the switch, which is fed from one breaker, and the rear unit is direct to another breaker. We removed the switch, and wired the front unit to hot wires that were in the switch box, and ran another romex from the rear unit's breaker to the middle unit's wires inside the box. So we have temporarily bypassed the rear unit completely.
Now, I've read lots of posts about being able to run all 3 units at the same time. But the way it is wired, that is not possible at all. We attempted at first to just connect all the wires in the box together and see if that would work (as many have stated it does). The 2 units ran for only about 3 mins before tripping the 20A breaker that they were attached to. Also, after looking at the wire gauge, that's probably not a smart idea either. All 3 units need their own breaker. We attempted to connect one to a 15A breaker that controls the fireplace (since it's June in TX won't be needing the fireplace for a minute). The unit ran for a while, but eventually overloaded the 15A as well. Any ideas on how to run all 3 together? My only thought is to replace the 15A with a 20A, but then I'd have to put the 15A back when winter comes and we want to use the fireplace again, so I don't overload wiring to the fireplace using an oversized breaker.