macbook pro shutsdown after removing power cord

i have a core duo 15" macbook pro with 1.5 gb ram and whenever i remove the power cord it automatically shutsdown (battery is 100% full charge). i bought the machine on september and i started to have the same issue after 2 months of use.

i took it to an apple store and they said it is fine and they didnt find any thing wrong with the battery. now its starting to do it again and ive also noticed a slight bulge in the middle of the battery near the check charge button. also, i used the coconut battery app to check its life (not charge) and its down to 75% already and it also says the age of my mac is about 1000 months! (what the?).

i dont want to take it to the store again, so if i call apple support am i likely to swap my battery for a new one? im feeling that all these issues point to a faulty battery and i am entitled to a new one that enables me to use my laptop without the power cord plugged in all the time!

thanks