I do not believe that "dissolve" is the correct term for what usually happens to mummies because dissolving involves water. But mummies can and do disintegrate (fall apart).
Basically, mummies are pretty fragile. After all, the Egyptian ones have been around for thousands of years. Something that old is pretty likely to fall apart. They have disintegrated from being kept in conditions that were too hot or too cold or too humid or that had too many insects. They have disintegrated when they were unwrapped so that people could look at them.
Mummies are fragile and are (in the case of Egypt) very old. Because of that, they disintegrate pretty easily.
I actually think this is a very interesting topic. It is clear that the question is poorly defined, but it is also a very legitimate connundrum. One, for instance, would like to state such claims as "steel evaporates" all the time, but it only does it in very slow fashion. Some, more rigorous physicists, may claim that is sublimation, but, the fact is, everything (no matter how rocky, or solid) actually "evaporates" to some extent. As long as molecules do come off the body and into the surrounding vicinity, you should be able to "smell" them, as they "evaporate".
"dissolving", as a change of state, will depend of the quality (and quantity) of the dissolvent.
Some substances are known as "hygroscopic", when they show the capacity to absorb humidity from the surrounding medium. There is a further condition, by which the referred substance not only absorbs the humidity but also DISSOLVES itself in the process, and such phenomenon is called "deliquescence".
Whether your mummies are, or not, subject to these processes, the only reasonable answer to your question is
"here lies Ozymandias..."
New Question: Do People Still Belive That Mummies Can Become Cursed?