I'm thinking it has something to do with the mirror box. I dunno if the KX has cushion in its assembly the way a lot of SLRs do, but after a while, these cushions deteriorate and can lead to various problems.
The KX is a classic workhorse and is, to me, one of those cameras that is worth spending the money on for repairs. If kept up, I don't see why cameras like the KX and others in its "workhorse" class can't last well beyond the century mark. Its tech is already almost 60 years old. (It has a lot in common with the Spotmatics of the 1960s). So yeah, I'd just find a competent tech and have it gone through. I wouldn't be surprised at all if it ends up being a simple repair.