From the description, it sounds like either beer stone or a silicate deposit.
Do you use PBW? Using too much over time will build up a layer of silicate that sticks to the walls and won't dissolve in acid.
Beer Stone is a natural deposit from minerals in your water. It is also a slow build up, but it will dissolve in various acids. This deposit is largely coming from beer itself, but can also be a reaction between alkaline cleaners, hard water minerals (calcium and magnesium) and protein.
Try wiping the deposit with a little undiluted star san. The phosphoric acid will dissolve light amounts of beer stone but it won't do much to silicate. If it is silicate (still powdery when it dries), you're just going to have to scrub it away and it can be tough stuff to remove.
In the long run, nitric acid is better at removing beer stone that phosphoric. It also can passivate the steel when used properly. For homebrewers, the easiest, safest source is beer line acid cleaner which can be purchased from Northern Brewer or Micromatic.