Ciao! If the hotels are offering parking at a nearby garage and they are both in the ZTL area, make sure to find out who of the two is sending the license plate to the police. It doesn’t matter who, but one of them needs to do it. Every time you drive into the center, it needs to be sent and, if you’re driving in, the hotel staff don’t know they need to do it unless you expressly tell them. The garage people will more likely do it automatically since you’re likely using the car on day trips, right?
In any case, just make sure the license plate gets sent every time you drive into the ZTL. It doesn’t matter when you drive out or once inside if you’re driving inside on your way out. But day to day, the “pass” you get with the license plate is for each time you go in and it gets sent , not for your entire stay and not a pass to do it all day in and out.