I haven't tested it on other maps or anything since I presume it's the same. If I vet a Pershing to Vet3, save the custom game (no mods), exit COH2, start it back up and load the said save, the Pershing will still have the 3 stars, but all the veterancy bonuses will be gone. No matter how much enemies encircle it, the granades won't be tossed. Reload will be 6 seconds (tested it on the King Tiger because I saved the game right as the experts called in 2 of them and my Pershing was already on Vet3). Don't know about acceleration because I can't really test it but it does seem slower. Steppes btw was the map played, 2 expert allies vs 3 expert nazis. Of course, US is the faction.
In a nutshell: Play US -> Call in Pershing -> Vet Pershing to Vet3 -> Pershing can finally beat Panther -> Save the game -> Exit game -> Start the game up some time later -> Load the said save -> Pershing loses (at least) reload speed bonus and grenade defense bonus (stars are still up, everything says vet3 except, it isn't) -> Start a new game and hope to finish it without reloading a save, or at least don't call in pershing and vet it before reloading.
It's really really annoying. Vet3 Pershing attacking a King Tiger with reload speed of about 6.5 seconds (error of about 0.2 seconds I guess, pressing the pause on my smartphone stopwatch)