Why will my iPhone 4S only work with a power supply?

Recently my iPhone will only operate when being charged. Once I take it off charge, the phone lasts for 1-2minutes (it is fully charged) and switches off. Then I try turn turn it back on, and it says it needs charging.
please could someone give a reason for why this is and also how to tackle it.
I will also give points for answers!

You may need to change the battery

The battery is obviously shot. Rechargeable batteries only last for so many charge cycles, and yours is at the end of its life. If your phone had an electrical problem, it would turn off immediately upon unplugging it rather than a minute or two later (though the battery may die the rest of the way and cause that same behavior soon.) The only solution is to take it to Apple and have them replace the battery, or order a third-party battery replacement toolkit and do it yourself (cheaper, but not recommended unless you're comfortable taking apart and putting back together small electronics), or get a new phone. Considering how much it costs to replace the battery, if your phone is eligible for an upgrade with your wireless provider, you should probably just upgrade to a 5s.