This feels exactly like your access system is updating the card’s user memory space with data and checking for that data next time it’s used. It’s a shitty security mechanic but it works to block this very thing - makes clones of access cards impractical and at best only have a very short window of use… and even if used successfully the original cardholder will know something is up because their card won’t work anymore… But nobody knows about this security mechanism or cares.
Anyway… if you want to test, clone your fob again and use your clone for a while… a week maybe… I’m sure it will work fine for weeks but your original fob will no longer work. Clone your clone’s user data sectors back to your fob and I’m sure the fob will start working again.