Is the outlet and/or plug overheating? If there's a bad electrical connection at the receptacle, the EVSE might shut down. IIRC, there's a thermal switch in the OEM EVSE plug that's intended to protect against a bad-connection-caused fire. A bad connection can be caused by an old and/or corroded receptacle, or bad wire connections to it. If the two outlets in the garage are the same (elderly) age, they could both be equally bad. Might require an outlet replacement. If that's the issue, consider replacing with a high-quality commercial grade duplex outlet, and make certain the wire connections to the receptacle are rock-solid, and properly pigtailed.
Edit to add: Make sure that in addition to the receptacle you use, all of the receptacles upstream (from the outlet you are using to the breaker panel) are in good condition, and pigtailed. By pigtailing upstream fixtures, you're not depending on possible bad connections, with the charge current flowing through old fixtures. If you don't know what pigtailing is, you might want to engage the services of a licensed electrician.
