While the combined load of the two motors is getting a bit near the limits of the ESC, the villan of the piece might be the battery. If that can't supply whatever the current is that is being demanded, the resulting volt drop could well shut the ESC down. And "battery" includes all of the wiring until you get into the ESC.
12 volts suggests SLA. While they are capable of very high current briefly (car starter motors generally work) they are rarely good for continuous loads. They were only used before later battery types became available because they were what was available. Under heavy use, they age rapidly.
Putting lower value fuses in the motor feeds could indicate whether they are overloading something in the power train, but be aware that to blow fast, fuses will pass a lot more current than their label states for some time. The easily got ones are not precision instruments. For that, contact breakers are better, but for weight, size and cost, two ESCs probably wins.
When selecting an ESC, the conservative way is to know the motor running requirement, double that, then go for the next ESC up. That moves the bottleneck.