Does the Single Edge rust?
The Single Edge is made from solid stainless steel, and will not rust. That said, you may notice rust appearing on the razor head if you leave it in a damp location for a long period of time.
When this happens, what you're seeing is actually a result of the blade rusting and depositing that rust on the handle. This tends to happen in places where water builds up easily (like between the blade and base plate). The easiest way to avoid this from happening is to give the razor a few good shakes after using it - and ensuring that you store it in the open so that it can dry. Storing it in a drawer (or worse, the shower) will almost certainly lead to the rusting you see over time.
Even a quick blow on the razor helps as well. Some of our customers go as far as to give the razor a quick dip in rubbing alcohol and allowing it to air dry. This removes all the water from the surface.
The following are best practices to prevent rust from appearing on your razor:
Next time the rust appears, clean it thoroughly with a cloth and white vinegar, if possible. If you leave any rust on the surface after it appears, it will come back much more easily next time.
If you have some mineral oil around the house, a few drops on the area after cleaning is helpful.
When using the razor, ensure you shake out any excess water and store it where it can dry.
Replace the blade every 1-2 weeks, or about the time you typically begin to see rust. All razor blades rust (even Gillette and Harry's) - it's just a matter of time and moisture. Pitch it before it rusts!