Depends on several factors:
* The brand/model of tube gear (high-quality or crapola toob du jor?)
* The type of design it employs and what role the tubes play in the signal path or gain stage (starved plate? hybrid? transformer input/output?).
* The kind of tubes it uses (12AX? 12AU? etc etc). Also, what brand? (Sovtek? Svetlana? Tung Sol? Telefunken?)
* Are transformers employed? If so, what kind? (Jensen?)
Most importantly, how are you using it? Are the tubes being driven hard or soft? Are they being used to impart a desired coloration to the sound, or are they merely performing their intended function?
What a lot of people don't realize is that most true quality tube gear is noted more for it's transparency, due to the lack of distortions otherwise imparted by transistors in solid state gear. The distortions that a lot of us find pleasing in some tube gear is mostly a result of guys like Hendrix, who figured out how cool it sounded when driving the hell out of tube amplifiers. Designers of other types gear followed suit by utilizing tube designs to achieve similar warm colorations for other applications.
So the question really depends on whether the tube gear you're using is intended to act as a fuzz box (ART?), subtle coloration (Peavey VMP2?) or if it was designed to deliver clean, full-soudning gain and/or dynamics processing (Avalon? Manley?). If all of the tubes in your signal chain were designed with the former in mind, then I think the answer would be pretty obvious that you might run in to tube fatigue, unless that is a special effect you are after.