cardboard
When put on charge, the battery app recalculates the percentage of charge left. The 1% indicates an estimation due to an intensive task or expectation. It probably wasn't at 1%. When put back on charge, it can more accurately predict the amount of charge. It loses battery quickly because it probably is at 30% when displaying 50%. It happens to me as well - my phone will die at 1%, and then turn back on itself a minute later at 30%. It's just a battery problem.
SRΛSC
Sounds like the battery is bad. Should let an Apple Store check it
BlkBear
Either the charging port or the battery is faulty, one of the other or both needs to be fixed/replaced. Time to call your carrier and ask them what the process is for getting the phone looked at or take it to an Apple Store and have them check it out.
damin
Sounds like your battery is shot
Anonymous
sounds like your battery is shot