Why does my battery keep dieing?

My car won't start. I used a multi meter and checked the battery while it was running and it was reading over 14 so I know the alternator is working. I check the battery after I shut the car off and it was reading 12.51 and then I go in the car, unlock and lock the car a few times then try to start it but it won't start. After trying to start I check the battery again and it is 11.77. I have been only driving short distances to and from work the last few months (15 minutes). When I used to drive 45 minutes to work sometimes my battery light would come on and then shut off. Haven't seen the battery light lately because I haven't driven a long distance in the car. I believe my drive belt may be loose too because it makes a chirping noise in idle. I have been meaning to get under the car and tighten it a little because I don't have an automatic adjuster. Don't know if this has anything to do with the battery. I just bought a new battery 3 months ago because I was having this same problem. I haven't had any problem until now. Normally I would think it is just a bad battery not holding a charge but I haven't had it very long. So I am a little puzzled. Don't really want to spend the money to buy a new battery I guess I should have kept the receipt for the warranty!