Most tube preamps do not pass a lot of current through tubes, and thus the circuit, per se, is not hard on tubes. The issue is that most tube preamps have solid-state rectification (power supplies), and when the preamp is powered up, the tubes are slammed by the sudden application of voltage. This beats up the tubes quite quickly, some preamps quicker than others (the Audible Illusions is a well-known example). With such preamps, the way to avoid this is to leave the preamp powered up 24/7. Some tube pre's offer a soft-start feature which applies voltage slowly (e.g., CAT's preamps), but the tubes are still subjected to deleterious thermal cycles if the preamp is not left on 24/7, as they expand and contract as they heat up and cool down in response to being turned on and off, which is very damaging to tube or transistor life over time.
The question is more complicated for tube preamps with tube power supplies, as tubes in the power supply can pass a lot of current and thus face the same wear issues that output (power) tubes do, meaning that you may face premature tube failure if you leave the unit powered up 24/7. In addition, as tube power supplies tend to apply voltage gradually, not unlike a soft-start feature, turning the unit on and off does not beat up the tubes like tube pre's with solid-state power supplies. Thus, a reasonable approach with such pre's is to turn them on and off.
Tube preamps with tube rectification tend to be rare these days and are almost all quite expensive. The issue is really for the 95%+ of tube preamps that have solid-state rectification. To restate the point about what turn-on can do to small-signal tubes (the type of tubes used in tube preamps), the Wikipedia entry for "vacuum tube" has this to say about operation of the Colossus computers used in World War II to decipher enemy radio transmissions, which each used thousands of small-signal tubes:
"The Colossus computer's designer, Dr Tommy Flowers, had a theory that most of the unreliability was caused during power down and (mainly) power up. Once Colossus was built and installed, it was switched on and left switched on running from dual redundant diesel generators (the wartime mains supply being considered too unreliable). The only time it was switched off was for conversion to the Colossus Mk2 and the addition of another 500 or so tubes. Another 9 Colossus Mk2s were built, and all 10 machines ran with a surprising degree of reliability. The 10 Colossi consumed 15 kilowatts of power each, 24 hours a day, 365 days a year—nearly all of it for the tube heaters."
The Wikipedia entry for the Colossus emphasizes this point:
"Colossus used state-of-the-art vacuum tubes (thermionic valves), thyratrons and photomultipliers to optically read a paper tape and then applied a programmable logical function to every character, counting how often this function returned "true". Although machines with many valves [tubes] were known to have high failure rates, it was recognised that valve failures occurred most frequently with the current surge at power on, so the Colossus machines, once turned on, were never powered down unless they malfunctioned."
