I would replace the rubber rim strip with a high-quality cloth one (Velox) or whatever synthetic version your local bike shop sells. While you're there, see if the spoke is too long -- that looks like a single-wall rim, so spoke length is more critical than on a double-wall. But understand that tubes do have a lifespan; friction, heat, and age will eventually wear them out. What you've experienced isn't at all uncommon.
And your bike doesn't look half as dirty as what routinely shows up in the shop where I work.
