I wonder if rubbing it with olive or vegetable oil would help.

Here's a wild idea that just came to me -

When new, or before getting rusty, I wonder what would happen if you dipped the metal item into a small container, something like an aluminum pie pan or disposable bowl, containing clear plastic resin to coat it thoroughly. You know, resin like the kind used for surfboards. I'm sure it's available in smaller sizes from a hobby store. You'd need to hang it up to set. If the plastic adheres to the metal, you'd have what you want.

On the same thought process as Elmer, I wonder if you could spray it with a clear coat of acrylic like https://www.amazon.com/Krylon-K05131307-Crystal-Interior-Exterior/dp/B000VKY3I4?ref_=fsclp_pl_dp_3

Just buy a solid metal such as brass and it won't rust.

I vote for the clear acrylic spray. I've used it myself and it is extremely easy to apply and fully waterproof if you apply a uniform full coverage (no missed spots).

ditto the rust-oleum!

take the time, and coat with clear fingernail polish?

The gold-toned one I had bought from Bath & Bodyworks rusted, too. I brought it back and exchanged it for a chrome colored one. I have another chrome one for several years which has never rusted.

All good suggestions above. If the sleeves are made of steel that has been plated with silver, copper or bronze, they will eventually rust as the plating wears away. Unless the sleeves are high end, plating on items such as these is notoriously thin and wears away fairly quickly. Either coat it right away (when new) with one of the products mentioned above, before the plating starts to wear, or buy something made out of metals that don't rust such as silver, copper, bronze. Keep in mind that silver, copper and bronze will tarnish unless they have a protective coating such as the ones previously mentioned. Many people value the tarnish (patina) and prefer to let it develop on it's own. Shiny or patina is a personal preference.