System runs fine when thermostat is bypass (out of system) installed honeywell heatpump system starts runs for seven seconds then shuts condenser off. Low voltage ?

You need to put a meter on it to find out what is really happening. You cannot guess at these things. It could be a bad coil in the contactor or low voltage to the contactor causing the amperage to go up and drop out coil. I have never seen this happen in 35 years doing this work, but you see something new every day. Check between R and Y on t-stat and between R and Common and let me know what you find. Also, remove coil wires from contactor on outside unit after turning all power off and read the ohms across coil and see if it reads to ground. If the coil reads low ohms below 1 kilo-ohm then it is shorted between some of the coils which is common on some units. A power surge can cause this to happen, or just age. Another problem could be that a safety like a low or high pressure switch is opening and dropping out power to contactor. See if it has safeties installed on Freon lines near compressor. Let me know what you find.(Safeties have two wires and are wired in series with supply voltage to contactor coil.) DrTom4444