This isn't a straight answer to your question, but to avoid these sorts of problems I use a separate midi track firing off a snare rimshot or similar as a click track.

I have clients that are not greatly familiar with metronomes say this to me all the time. Get a little korg $20 one and see if it does this. If it does it is the user. If it doesn't more investigating will be needed.

The only way a daw clicktrack changes speed is if the tempo setting is changed manually or via automation. A third possibility is that the computer chugs or stutters but the tempo will remain constant.
As a professional musician and teacher, I can tell you unequivocably that most people have to LEARN to play with a metronome and are completely unaware that their tempo is not constant. Especially if they try to sing and play at the same time. They will swear otherwise on their life but are dead wrong.

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Thanks for your responses gang!
Paul, I do have a small Korg MA-30 Metronome. I've had it for awhile to practice my timing. Haven't had problems with this; and I always make sure a new battery is installed every 2-3 months.

One thing you can do is go into a program like Fruity Loops, create your own click and then export it. There'll be no latency problems and you'll have a separate MP3/WAV that you can insert into your session. It's also good for when moving projects around different DAWs, as each DAW's inbuilt clicks always seem to be ever so slightly out of sync with each other.