If this is a new install then double check proper wiring for high voltage (460v) that the correct taps are put together and such, if it is an existing install that was running fine but then started having problems, check for single phasing all the way to the motor, do not check for single phasing by metering from phase to ground or you will just see the back fed voltage from another winding, go A-B, A-C, B-C for proper voltage, also check the current on all three phases, you could have a bad tip on the contactor that allows the first start up but after that one of them opens up after it has heated up, this can also happen on the overload heater elements if they are the heater type and not electronic.
If this is a positive displacement pump such as a pressure washer or other high pressure application then check the unloading valve to make sure it unloads the head pressure when the motor shuts down, this may be in the pressure switch or one in the head that uses the oil pressure to close it like on an air compressor, Is there a check valve after the outlet pipe? maybe it is sticking shut?
I'm leaning to a single phasing issue like the others specially if this is a centrifugal pump.
Also does this motor have a WYE start delta run starter? (6 or 12 lead) or is the motor a 12 lead but is wired in a WYE, if it is a 12 lead and you are using a DOL starter then make sure the motor is wired for delta.
Try to ohm out the phases to the motor right when it doesn't start but make sure you have removed the power, this could show up a winding opening up from heat, if it takes 10 to 15 Min's before it starts back up this sounds like a heat issue that is opening one phase to the motor or in the motor winding.
One more thing, if you find that when it is not starting and you confirm it has high current on all three phases then you might want to look for a mechanical issue such as seals or bearings binding from heating up after the motor has been running, it might take using three amp meters to catch this if it trips out faster then you can check each phase, but you must make sure you have high current on all three phases to be sure its not a single phasing issue.