Ive just got a powercap and stock battery (which is about 3 years old now) and holds its charge with no problems, with alot of punishment. I even play it with the engine off sometimes and still have no problems.
As alfie says, the powercap wont solve your power problems. IMO it stops a bit of dimming depending on music. If its continious bass it wont matter because the cap has no chance to refill. What they do primerily is hold the whole car voltage up on large bass notes - If the note takes more power than the cap holds, you will dim.
Uprating the Alternator will stop dimming, and an uprated battery will keep the system running for longer
As for your amp being 1000w, thats about 500w RMS (assuming 50% efficiency) so woulnt kill your battery that bad. (Im running about 1200 RMS with little problems on my tiny 45 Uno)
This reminds me i must update teh power issues tutorial
Hopefully, what Gaz suggested may be your problem. Only way to find out is to get teh battery checked. If it does need replacing, i wouldnt worry upgrading to an Ultima unless you have deep pockets and plan to put alot more power into the car. A split charger as recommended by one of your mates could be a way forward, but if you uprate the alternator there should be no need
Hope thats cleared some things up