A "Last Update Failed" message is often (albeit not always) an indication your device believes it is at a higher firmware version than the 'upgrade' being attempted. Suggest the following:
- restore your original build.prop (you made a backup, right?)
- attempt an upgrade to 3.2.5 using bin and instructions
here; if the update doesn't take try a factory reset per guidance from
@travanx
- once at 3.2.5 you will need to reroot (suggest
HDX toolkit) and block OTA if you need to temporarily connect to wifi
- follow the guidance in the OP to downgrade from 3.2.5 to 3.1.x (lower portion of post; don't mess with build.prop)
I assume your device shipped with 3.2.4 or naturally upgraded from a lower version via Amazon's normal OTA process.
If it still doesn't recognize the 3.2.5 bin as an update then something is likely messed with build.prop and/or a previous attempt to block OTA updates that hasn't been fully reversed.
As always be sure to remove all wifi profiles and stay away from open hotspots so your device can't spontaneously connect. Once on 3.2.5 Amazon will attempt to push 4.x updates which you clearly do not want.