Depends on what the base cause is. If it's a resin prop, it could be the resin wasn't correctly cured and it's bleeding out causing the paint to not adhere correctly.
If it's not resin, then the paint was either old or not properly shaken.
So, here's the fix. Take some Simple Green (NOT soylent green, that's made from people and it's hard to wash off) or ez-off oven cleaner and test it on a small part to see how it reacts. The paint should come right off.
Now, if it's resin, give it a good wash in warm soapy water and let it sit for a few days after you've dried it. If it's not cured, it'll feel oily. If it is cured, then it was just bad paint. If it's not cured, you can try putting it in a 200* oven for a few hours and hopefully, that'll work. Then prime and paint as normal.
-Fred