I have Fender Hot Rod Deluxe and Blues Deluxe amps.After the amps are in use for 20-30 minutes, volume just flat out fades to almost nothing. I have had it checked out and technician could not reproduce the problem, however, he said it was a known issue with these amps. Tubes are OK. What gives?

Most likely clipping. This happens when the source DBs are too high for the amp....feeding in too hot.

The Fender Hot Rod Deluxe shows a 2-button footswitch as standard but I'm confused. This link shows it as connected to the amp via a mono cable ... FENDER Hot Rod Deluxe DeVille Footswitch which is impossible using two switches. Normally it's a stereo (tip, ring, sleeve) with tip to sleeve being one connection, and ring to sleeve the other. Good luck with this one.

If not a valve issue check by preamp valve substitution 12AX7A's.Check solder joints +/- 16v circuits and send/return and input jacks.

This is because your clean channel only runs through the pre-amp section, requiring an increased volume level to match that of the volume of the drive section which is overdriven by the pre-amp circuit. my suggestion is to use lower volume level on the clean channel of the amp. To get any volume boost you may need to match the two channels you could use a signal/volume booster or overdrive pedal between your guitar and amp input, switching it off and back on when you switch back and forth between channels.

Realize that the number on the volume control is only relative... it means nothing regarding what the amp can produce. With a high level output guitar you can easily drive the amp into distortion at very low volume control level settings... what counts is the actual output sound volume and specifically the voltage output going to the speaker. Once the amp reaches saturation, any further input just pushes it into distortion or "flat topping".
An oscilloscope on the output will quickly show when amp starts to flat top.

CHECK VOLUME CONTROL BUTTON.

You can plug the output of the gt10 into the "power amp in" jack of the Fender. This bypasses the preamps in the Fender but uses a buffer amps in the Fender to drive the power amp. Please note that the reverb is STILL in the circuit when you do this. You can turn the reverb to zero if you wish to disable it.

Fender hot rod´s have an common problem on the plate resistors of the preamp and phase inverter tubes.

Check if the 100K and 82K resistors on the tube socket board are not brown. Those resistors usually need to be changed to bigger ones 1/2W.

this guy made a good document about this fix:

http://home.comcast.net/~fredholz/Justin-Holton/Fixing%20Loud%20and%20Intermittent%20Crackle%20or%20Static.pdf

i am guessing on what the problem is , the post is very vague. i am guessing a channel switching issue. you need to check the "sugar cube" looking power resistors solder welds. they are probably cracked and arent making good contact. if you tap on the amp it will cut in and out, its probably these two resistors. they are usually 470ohm 5 watt cement resistors. what happens is they get real hot, and as they cool down they crack the little solder welds. i usually replace them with new and keep them floating up over the pcb to help them stay cool and off of the board to prevent further solder weld cracking, stock they are real close to the board. then put a little silicon under the resistor to hold it in place and to keep it still on the board. i just fixed a blues deluxe with this issue. while you are in there, cut out the resistor sitting right behind the reverb pot, this will make the reverb awesome. also solder the mid pot center leg to the mid pot leg that comes off of the bass pot leg to get better midrange control. very easy mods. check the master volume pot, is it a B100K? pull it and put an A250k in its place for better volume control. bias pots , etc. check my website yostamplifier.com.

More than likely a bad solder joint. Where is the next question. How confident are you with voltage measurments? The rails in tube amps are high and can kill you so if you are not inclined to do so please don't. The reason I suspect a solder joint is that it is a failure over time, cold solder joints expand and contract with heat. When they heat up they break connection. Not saying 100% that is your problem but it is very likley.