your battery is just a reserve.. When you calculate the entire load of your car when running complete with headlamps, A/C etc - your load is like 35 to 40 amps already, which the alternator is sweating out for you...
When you tax it more - it cant and your juice needs to come from the battery effectively killing it because it cannot be topped up by the alternator itself. Ergo you need a bigger alternator on your engine, something like 65 or 70 amps to suffice the demand of the car. It will do nicely - more nicely if the alternator says - BOSCH, VALEO (France) or Motorola on it (tough to find and a little more than tough to fit if you dont have a fabricator freind)
On a nicer note - you can buy a Denso or Mitsubishi alternator that will fit easily.. use the same 45 AH slim battery your car came with but be sure to use proper electrolyte in it and install the larger alternator, it'll work sweetly