On my previous Outback travel trailer, a tire went flat in my drive way. I REALLY did not want to purchase new tires, as mine were still, almost brand new and installed (like a month) previous).
I talked to my neighbor (we live in farm country) about the tire and he looked at it. He said it was no problem. They have flats all the time on their BIG RIG tractors and combines and they simply plug the tires. We're talking tires that cost $5,000 each. (big suckers).
He said he could fix the tire and I'd not even have to take the tire off the trailer. He got his tire plug kit and plugged the tire. I was skeptical, but tire held air until we sold the trailer years later with thousands and thousands of miles.
What's more interesting? The "plug" kit he used was one of those simple tire plug kits purchased from Wall Mart or any automotive parts store.
When I was 15 years old, I worked at my Uncle's gas station. My uncle taught me how to plug tires (this was before the day of "steal belted"), but tubeless tires were just becoming the new standard for tires. If a tire was too bad off to hold air, we'd put a tube inside the tire and everyone was happy.
Now... automobile tire shops will NOT do that today. In fact, they won't plug tires either any more. Noooooo..... they want you to buy new tires. That's more money for them.
Where am I going with all of this? Simple. Follow artfuldodger advise above. But.... if you have your own air compressor, then it would not hurt to pick up a tire plug kit and keep it with you in the camper, in your box of "stuff" for camper repair. If the tires looses air, try plugging first before purchasing a new tire.
Once the tire runs a few miles, the little rubber that sticks out on the outside of the tire will rub off and the plug will never be seen. If you tell no one, no one will ever know it was plugged.
If you do plug it (because it lost air), and it still looses air AFTER you've plugged it .... then yes ..... get a new tire then.