When we moved our domicile to a mail service, their signup documents included a provision that they would not accept refrigerated packages. They don't have a place to store then, and the mail service knows that folks can easily go weeks or even a couple months between mail forwarding.
We usually have our mail forwarded every two weeks if we are in one area for a long time. Otherwise I try to pick a small town where we will be for at least three weekdays and have our mail forwarded to general delivery. Twice I've tried to have our mail forwarded to a post office in a large city, and both times it took a couple extra days to get the mail.
Even with a priority mail tracking number showing the package had arrived at that post office.
Almost never do I find / stay at a campground/ RV park which will accept mail. UPS and FedEx packages are easier to get most places. In populated cities there is often a local office where you can have the package delivered for pickup, or a store of some type which will accept those.
Our problem with medicine was that it is impossible to tell when our mail order pharmacy will actually send the shipment out the door. And we never get tracking info from them until two or three business days after shipment. We usually get notice of a package arrival at our mail forwarder before we get notifications that the pharmacy shipped something.
I have been able to call my mail service at 2 pm, and have them send a specific drug to us via FedEx overnight that day. We got it at 8:30 the next morning. A more expensive than normal shipment, but our fault because one of us neglected to check to make sure a prescription was refilled on time.
If a person is in the habit of not refilling a prescription until the last onhand dose has been taken, mail order pharmacies and traveling will take a new mindset.