However, as it most apparent on complex, avangarde jazz pieces (Kith Jarett, Jan Garbarek, Chick Corea etc.) it looses musical connection (?) It does it on any kind of music, but on regular music it is less obvious, because it still have enough "melody (?)" left to connect sounds into music(?). When switched to any other, out of 5 preamps, (cold, SS or whatever) which BTW, have less of extensions, clarity etc.,, the music comes back. So, the correct word is probably musicality not emotional engagement?Usually tubes have lower distortion (after all, they are quite linear). However, a lot depends on execution- and the tubes in the unit. You might have them tested for starters; a bad tube might do OK on simple material and might fall apart when things get complex.
Other brands might work better too.
Also there is the design of the line section itself- they are not all created equal and some are pretty bad- as George points out, they can be prone to colorations of their own (usually the distortions found in tube equipment are of the lower harmonics, which the ear converts to 'warmth'). But if there are design flaws all sorts of issues can crop up.
I would start by getting the tubes tested!

