If this is a straight razor, may be mead of carbon steel and it can rust. If the rust does not affect the edge, you are OK. If it does affect the edge, then you need to hone it out.
Since you mentioned a blade, I presume you are talking about a DE or SE razor. Since these razors are not made of steel, what you are seeing is not rust. Razors are typically made of brass or a Zinc alloy that might be coated with chrome or nickel. If you are seeing corrosion, you probably have zinc alloy razor. Once the outer coating is pitted, the zinc underneath will start to corrode. If the corrosion affects the alignment of the razor blade, that could be an issue. If the corrosion is on the safety bar or edge of the cap, it might irritate your face. If the corrosion is elsewhere, it is primarily a cosmetic issue.
You can prolong the life of your razor by cleaning and drying it after your shave. If it is a three-piece razor, lubricating the threads with mineral oil or petroleum jelly can help protect the threads as this is often the point of failure.
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