Iphones check to see if there are any non apple components after an upgrade. Non OEM batteries are the target. If you have replaced your battery the phone will work fine until you do a software upgrade. When you do the upgrade, shortly after your phone will detect a non OEM battery and shut down completely. You will get one of two responses. A completely dead screen or, when the charger is plugged in, apple logo and nothing else. You can get Itunes to recognise the phone but it will refuse to do a restore.
Replace the battery with an OEM battery and the phone will be back to noemal. Don't we love Apple!