It's is "normal" or common. Many of the shops these days will charge you for a re-inspection. You have to ask questions before you do business with them. Ask if they charge for a reinspection. Also ask about the time frame. You don't have forever to make the necessary repairs and get the 2nd inspection at no charge.

I don't know anything about your car, the situation, or the shop. However 60 days is not reasonable. I know you said <60 days, but 30 days would usually be too much time.

Another hint- Don't bring an old car to a dealership. There are also other shops that don't want to bother with old cars. They will just fail you perpetually until you go away. More honest shop owners will tell you.