You need minimum 5.6.1.1 firmware for the original Paperwhite (5th generation per Amazon nomenclature) to connect to Amazon.
https://www.amazon.com/gp/help/custo...deId=202048000
Jailbreak is persistent after you update. Another good thing is downgrade is always possible so you can always rejailbreak if needed. Can't remember all the steps anymore. Just check out the various tutorials relevant to your device.