Yes, go hunting for a bad connection first, in a case of odd behavior like this.
Tuner cleaner is a good weapon, too.
How hot are the components when you land?
Yes the logger in the ESC will tell you its own max temp, but it warns you as Crist said.
Also be wary of having any of the low current wiring (like the timer to ESC wires) running too close to the high current wires at either end of the ESC.
Noise coupled from the high current wires can confuse the ESC input and it sometimes responds by politely sitting on its own hands.
later,
Dean