This is mostly a digital amp which uses the tube for distortion, but not the same way as all-tube amps. Maybe we can help you, but there's a good chance this problem
isn't related to the tube.
I found this service manual for an older/smaller Valvetronix:
http://www.valvetronix.net/docs/AD15_30Servicemanual.pdf The exact schematic would be helpful. Not sure if it's available.
Based on that possibly-wrong info? The 12AX7 heater is run separately from all other parts of the power supply, so it's no surprise that it works while an unknown number of other things stop working.
Also, there aren't high/low voltages for the tube and SS parts, only 2 voltage levels in the power supply. The tube's non-heater parts run off the same "low" voltage of +/-20v (later lowered to +/-15v) as other discrete components, including the SS poweramp. The computer parts run off +3.3v.
So I'd inspect any part of those low-voltage power supplies that you can locate. Find somewhere to check their voltages. If you're lucky, it will be correct when the amp's working and zero (or very low) when it stops working. If it's just a power supply problem, that would confirm it. You can then check the rectifiers, capacitors, physical connections, and regulators in the power supplies. I'd expect the newer, larger amp you have uses different components for basically all of those functions, but a similar overall design.