Everything that goes wrong starts with putting it away damp
Warm, dark, moist and soft is a description of a growth medium.
Rinse the sleeve through with warm water, let the water run both ways, and then leave it out until it is dry the whole way through. That takes hours rather than minutes, and it is the whole of the maintenance. A sleeve put back in its case while it is still wet is a closed, warm, dark container with moisture in it, which is the standard recipe for mould.
The smell is the first sign and the last warning. A sour or musty sleeve has already grown something, and because the material is porous it cannot be sterilised back to new. At that point it gets replaced, which costs less than the alternative of using it.
What to do with it
Rinse it straight away, shake it out, and leave it somewhere with air on both ends: over the neck of a bottle, on a drying stand, or simply hanging. It needs hours, so the evening it is used is the evening it is left out.
Do not put it back in the case damp, do not dry it with a hairdryer, and do not use soap inside. If it ever smells sour, that one is finished and no amount of cleaning brings it back.
The same rules apply to everything else in the drawer: see cleaning and storage.
