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Welcome to iMore! Does your iPhone 4 still have its original battery? Apple's iPhone batteries are designed to retain 80% of their original capacity for 500 full charge cycles. After that you're on borrowed time.
The battery in my old iPhone 5 will sometimes discharge way down, and when I try to charge it, it takes an hour just to start showing the battery on the screen. It's on charge cycle 1154 at about 30% health. They do fine down to around 50%. Then it begins. The 4 is old now. If you can't possibly upgrade, at least buy a new battery.