Well, if it just clicks that sounds like battery or the copper connections inside the starter solenoid (the one attached the the motor). But that wouldn't casue it to shut down the engine after 10 mins of operation..... It *may* be a heat issue, if its air cooled check that your cooling fins are clear of any grass/dirt. If water cooled check the radiator/thermostat as it may have an over temperature cut off.
If it would just die and refuse to re-start i would suspect spark plugs, but that doesn't account for not even turning over.