I have noticed recently that my staff have begun disappearing from the staff list.
It seems to happen when they want a pay rise.
I give them the rise, but they disappear anyway.
Is this a new bug that has been introduced?

Considering the publisher and how old the game is, I doubt this is a new bug.

Now I haven't ever played the game, but perhaps you'd want to look into CorsixTH which is an open source reimplimentation of the TH engine, which might possibly fix any such mysterious issues.

(Someone more informed of the game might be able to root out the actual issue.)

How soon do they disappear after you've upped their salary? Staff usually demand a pay raise when their happiness level sinks too low. My best guess is that even though you increased their pay, the conditions that made them unhappy in the first place remained unresolved, and they eventually quit. I'm not 100% certain about this, but that's what I gather from my own experiences.

They won't disappear when given the rise, they will ask again if happiness drop too low again.
Are your machines well maintain and not exploded?
Staffs are killed if they in the room with explosive machine.