Factory resets, as well as account login/logout, wipe the Kindlet developer keystore, which we need to run KUAL, since it's obviously not signed by Amazon, but by ourselves

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The latest JailBreak/MKK should be more resilient, and a restart (or two, not quite sure of the timing in case of a factory reset) should put things to order.
Note that if you wiped the backup folders from the userstore, then you're not protected from a factory reset, only from account login/out. In which case, simply reinstall the latest JB (or bridge, which is potentially easier on FW versions that can't be jailbroken) and restart the device.