If the pump pulls close to 15 Amps, then you may want to replace the breaker with a 20 amp (after trying a heavy duty cord first). Although, it should only pull that at startup, tehn be down around 5 Amps.
Is the pool circuit isolated or is there a possibility that something else is on it thus pushing you over 15 Amps.
Have you checked your GFCI rating, it seems awfully strange that the 15A breaker goes before the 15A GFCI - almost points to a suspect weakened breaker.