Just simple ones, like tube degradation, low power, limited ability to handle less than 8 ohm loads, bass overhang, rolled off high frequencies, quality tube availability, high cost of power tubes, need for a vacuum tube tester, tube biasing, tube matching, sound variability dependent on tube brand or date of manufacture, total tube failure, high heat and overall reliability.
I understand that all of these rarely apply. But every one can be a possibility and therefore a trade off. Oh, and I forgot that sometimes the tubes needed go out of production. The stock pile of NOS is not going to last forever.
If you don't mind me debunking this at this late point in the thread:
Tubes do degrade, but if you stick to triodes the degradation is much slower.
Yes, tubes make less power, but that really isn't a problem as we shall see.
Its pretty fair to say that no amplifier really handles less than 8 ohms all that well. The problem here is that as load impedance is reduced, the distortion of any amplifier goes up. You might think it 'negligible' but its not; that increased distortion is almost entirely IM and higher ordered harmonics, both to which the ear is keenly sensitive. So the result is less detailed, harsher sound. Put another way, if high quality reproduction is your goal, your amplifier investment dollar will be best served by a loudspeaker that is 8 ohms or more, all other things being equal. A simple way to make any solid state design sound smoother and more detailed (due to less distortion) is to simply increase the load impedance. What I'm talking about here is the difference between a good hifi and something that sounds like real music.
There is no reason high frequencies have to be rolled off. The H/K Citation 2 had bandwidth to well over 60KHz; our amps go up to 200KHz (with full power to 1 Hz). It might be though that you hear less energy up high for a different reason- the ear converts distortion into tonality; higher ordered harmonics are perceived as brightness. If they are masked as they often are in a tube amp, the result is a perception of less energy even though the bandwidth might be the same. IOW the brighter sound you hear from solid state is often just distortion that isn't masked.
Bass overhang isn't a thing if the design is at all competent.
We get our power tubes from Russia; they cost tested at retail about $28.00 each. That's really not crazy money. We don't need a tester to test them; they can be tested visually- just by looking at them you can tell if they are good (and how they behave in our amps). BTW this is true of a lot of power tubes. Our bias and that of many other amps is automatic. We don't match the tubes- we've found no need but this is an issue in many other designs. We don't find a lot of variance between the Russian and Chinese variants; the American tubes sound a little better but are often less reliable (counter to how that sort of thing usually works with tube amps).
One thing you might want to keep in mind is that quite often these days its easier to find a replacement tube than it is to find a replacement semiconductor. There are millions of different semiconductors in production and that have been produced; of the latter many are obsolete and no longer available. We had a Classe amp in for repair some years back; what stymied the repair was that the output devices weren't available even from Classe. But that particular amp was made in the early 1990s and while almost any tube amp made in that time you can still find the replacement tubes, this decades on after tubes were declared 'obsolete'.
Reliability is an engineering issue. You can design for a given tube and depending on how you do it, the tube may or may not last. This is true of semiconductors as well, but since tubes are bit more forgiving (if you overheat one but let it cool off properly it might still be OK; don't do that with a transistor...) you can often get away with quite a lot. At audio shows I often short out the outputs of our amps, pull tubes while the amp is playing and the amp acts like nothing happened. Don't do that with a solid state amp!