How long did you have it before it failed?
I only have a couplefew electric tools from HF (angle polisher and 1/2" impact drill & ?) . They were very cheap & I had low expectations for longevity but have been pleasantly surprised. -Not put to great deal of use so far , but no failures and work quite well. If they do happen to fail any time in the future they would have exceeded expectations and provided quite decent value for the buck. Like many of us, for tools I use a lot more I pay the big bucks for good top name brands even though cost per use may end up greater even over time. And for that premium cost there is also at least a higher expectation I may be able to access some replacement parts if needed and desired. It's all a pretty obvious trade-off and we apply the odds according to our needs, preferences and affordability.
Do you happen to know anyone in the NSA or CIA who is fluent most forms of Chinese? If they are still using felt rings in the little compressors, there must be some way of tracking down the place that makes them and purchasing a few if you still have a yen for that, but with your determination I'm kind of amazed you haven't tried patiently making some yet, if you haven't. Do you know what thickness and material the old rings were? Any chance the inner and outer circumference matches any cans you have, to cut around, then soak the felt with Teflon lube?
Here's 1/4" thick sheet felt(wool) at Grainger. They have other thickness and polyester too.
http://www.grainger.com/product/Felt-Sheet-2FJA9?s_pp=false
But perhaps the originals were fabricated with fiber "grain" following all around the circle for added strength , unlike the sheets?
If you figure out a way to make your own effective felt piston rings , you may be able to corner the market to all the millions of other ring-needy HF customers worldwide! This could easily lead to top-notch healthcare for you and Mrs. Pucker, new fishing tackle and shiny new boat and motor, heck even a paid captain and crew !!
BTW- If you are curious to know the rather quite surprising variety of animals felt can apparently be made from , ...just Google "felt animals."