Of course, one can substantially increase the magnetic flux only for a short period. Hence the need to time the incoming projectile and the activation of the field precisely.
Probably wouldn't be effective against projectiles made of non-conductive materials then. However, it would be very difficult to make projectiles out of such materials that could penetrate modern armour.
Maybe another tactic for defeating the system would be to use a decoy closely followed by the real deal before the capacitors have a chance to recharge.