Fly Stim,
The IAM did a study on the effects of coffee on flying some years ago as I recall. I got caught up in it at the time as the crew room coffee machines became de-caff only (and worst of all, TEA was banned!).
The principal finding was that caffeine withdrawal set in about an hour or so into the sortie for heavy coffee drinkers, later or not at all for modest or light consumers. The effects were similar to tiredness, in that there was a loss of concentration and increased tendency to make more minor mistakes.
IIRC, these effects went away when the task got stressful, presumably as adrenaline cuts in and wakes you back up.