Nothing about this problem as described screamed out to me "bad capacitor".
With the intermittent operation of the condensing unit as described it appeared to me to be a bad connection in the wiring, bad t-stat or (now off the table) bad contactor.
Of course for all we know his unit has a HPS that is tripping due to a bad condenser fan motor.
Just not enough info was given to recommend changing parts IMHO.