After mentioning how much I like using a brass sponge when soldering, I came across this App Note from OK International. This is a great note to read through. It discusses what is inside of a soldering iron tip, why they fail, and how to keep them in good shape.
Image from OK International’s Tech Note
The note actually makes me realize two of my own mistakes.
First, most cleaning should be done with a wet sponge not the brass sponge. (Oops!)
Second, pre-made tip tinners are meant for occasional cleaning. Moving forward I think I’ll modify my soldering behavior so that I start with a quick clean in the brass, use the sponge while working on a board, and then use standard solder to protect the tip when done.