Carvin Vintage 50 buzzing

FWIW, A computer puts off a LOT of EMI.
If the amp (or guitar) are in close proximity, you're going to hear noise.
Some models will pickup more than others.  High Gain will typically be more noisy.
This was way worse when we were all running CRT monitors.
Single-coil pickups will (as you'd expect) pickup more noise.
 
Some guitars will also pickup WiFi related noise (if the router is close).
Wireless mics can also pickup WiFi related noise. 
If you play live (where digital mixers controlled via tablets are all the rage), you'll likely experience this.  
The stuttering noise matches the flashing LEDs on the router.
The solution is to separate the wireless mic receiver and Router (the more distance the better).
 
You need to separate the guitar amp and the computer.
 Wireless keyboard, wireless remote control via tablet, controllers like Fader-Port/Machine/Komplete Kontrol, etc... can be used to control your DAW's transport (allowing you to put distance between the amp and computer). 

Is the hum still present when any nearby, say under fifteen feet, computers, screens, TVs etc are switched off?
 
Hum might be an earth loop through the mains, but I doubt it* unless the amp is connected to the PC/audio interface by a cable, such as from the line out. If that is the case, does the hum go away when the amp/interface cable is disconnected.
*meaning it might still happen, but it's quite a lot less likely to.
 
A constant level of hum sounds like it might be coming from the amp's power stage which is almost certainly after the master volume control. Does the hum go away if the volume is turned down? If not their might be a problem with power stage valves or the output transformer.
 
All amps hum a bit, and valve amps also often have "blow" - a white noise kind of sound a bit like a high wind which is normal for valves, but different valves can be worse for it than others. A 50 watt amp is pretty loud and any noise it generates itself is going to be correspondingly loud. If the noise enters or is caused by the circuit after the master volume control then it's going to get the benefit of the full 50 watts the power amp shoves out

Update, the hum will go away after playing for about 30 minutes, but then, the volume will dip significantly... been looking around for answers, grounding or tubes seem to be the most commonly found cures, any addition suggestions?

Plugging everything into the same outlet/power strip DOES NOT fix ground loop problems as previously stated. 
 
As far as the original problem, I would suspect a bad tube.  I used to work as an amp tech and tubes can fail "anytime".   I have a Carvin BX500 amp that has a 12AX7 tube in the preamp section.  It failed (started some distortion) in less than 6 months and it was replaced by a NOS RCA 12AX7.  That was about 2 years ago.

I suggest talking to Carvin.

The only time I've seen an amp start out fine then after a while drop in volume, and in the case of that particular amp intermittent short cut-outs was a Marshall JTM30. An amp Marshall nowadays don't even own up to ever making.

The problem with that amp was a poorly designed and under-specified output transformer that overheated and did all kinds of strange things.