What could be causing your kitchen sink drain to stink like sewage occasionally while all other sink drains are fine?

The drainpipe under the sink should have a "U" shaped bend called a P-trap. Its purpose is to always hold a small amount of water in it which will block sewer gases from coming up through the sink and into the living space.

The problem could be:

No P-trap at all, which is unlikely.

P-trap water has evaporated from prolonged lack of use, unlikely in most homes.

The P-trap leaks, which may permit sewer gas escape.

The P-trap is dirty and needs to be removed and cleaned.

P-traps are not maintainence free. It would be a good idea to remove and clean them after years of use, and you don't need a plumber to do this if you are reasonably handy. And in the meantime, occasionally pour a little bleach in your sinks before you go to bed.

ANS 2 - Remove the P trap and clean it and the pipe above it thoroughly. If necessary fit a new P trap.