Every rim needs tape and sometimes replacing the rim tape can cure those mystery flats. Velox cloth rim tape is much better than plastic or rubber for preventing pinch flats so next time you replace your tubes try putting some Velox cloth rim tape on there as well. Enough for a single rim.
I've used the Velox brand rim tape for over 40 years and will continue to use for another 40 years that's how much I like it. I've had other brands of tape that came with various wheels when I bought them and just wasn't satisfied with any of them, so when replacement time came I would go back to my old standard tape...Velox. It's the easiest maintenance thing you can do to a rim. Always have a spare set of Velox tape on hand just in case.