If it happens only at a venue, this sounds like a circuit that is loaded to the edge of having the breaker blow. What you might be experiencing is the breaker almost halfway tripping. Some gear can sort of tolerate this, but some is very sensitive and will cut out. Next time I would just bring an extension cord, pick a different outlet to plug into, and hope it's on a different circuit. Try the one the guitarist is plugged into.
This happened once with my X32 digital mixer. The PA amps played on, but the mixer would drop its main fader to zero when it detected the power hiccup. Not fun. Moving to another circuit fixed it.