I can only reflect on the issues I had with mine. May not be the same problem you are having but sounds so close. When I first got the Mark V (head) I played for hours every day and used the 45W setting all the time. Also used the Variac mode more than full power as it was not as bright that way. The 90W was too loud for me at the time. The amp would cut out but in CH3 so the rectifier was automatically bypassed. I also found the Diode to sound better than the tube rectifier in the other channels. Within 2 months I was having issues and blew out the first set of tubes. That continued to happen with new tubes when I used the 45W mode. After the amp went dead with a burning smell, turns out I had damage to one of the screen resistors that literally split open. I doubt that you lost a screen resistor yet as the amp will not operate without it since the fuse will continue to blow out. Prior to loosing the screen resistor (happened in 45W mode with a set of JJ 6CA7 uses the EL34 bias setting) I have had no issues for 8 months of hard use in 90W mode which is a Class A/B mode) The 10W mode is a pure Class A circuit where as the 45W mode operates in extended Class A. You may notice the plate on one tube to begin to glow red at the seams (similar to a 6V6 tube which is normal for a 6V6, not a 6L6).
What I would do, sit next to the amp but have the front facing away from you so you have clear view of the power tubes. Play the amp as you normally would do but watch the tubes. In 45W mode, only the center two tubes will have a blue hue, the others will just have the orange glow of the heater element. The plates should appear dark in color. Best if you do this in a dark room or minimal light. continue to play though the amp unit the symptom shows. If one tube turns red hot (the dark metal plates are actually glowing red, aka "red plating"), or if you see a flash or arc in one of the tubes (sometimes the Rectifier tube will arc and if it does the power will drop and take a while to build up which may be the issue here). Replace the rectifier tube if you see lightning inside the tube (also note, the rectifier tube will not have a blue hue or glow to it which is normal).
If you have a power tube that does not have a heater glow, or it is really dim compared to the others there may be a fracture in the tube, however if it has a blue hue to it when playing it probably is ok).