The key here is that somehow guitar and mic are interreacting and causing feedback. Now as René pointed out, the mic and the guitar can't work together to cause feedback in the normal sense of the concept - they are both transducers, and for feedback you need a transducer and a speaker (technically another transducer, but I don't want to muddy the issue. Oh! Wait... I just did! ;D ).
If he's DI'ing the guitar, he must have some form of monitoring to hear himself, so Mr M's idea that there might be a monitor of some type involved is correct (could be a monitor, it could be a main positioned so he can get some spill). So this means it could be either feedback from speaker to guitar or from speaker to mic. Volume levels that cause a guitar pickup to feedback (primarily an electromagnetic transducer) would have to be really high, which makes the (electromechanical) mic the prime suspect.
So the question is how does one system (Guitar/ V-Amp) influence the feedback of (mic/PA) another? Mr M was thinking along this track when he assumed that it was the electrical coupling between the guitar and the mic at the PA amp. Spyke spoke about the off-axis mic response, which may also play a part, but isn't the whole picture.
My response was as follows:
Hi M***
For feedback, you need a sound source (like a speaker) and a transducer (pickup or mic) which are both part of the same system. The transducer picks up the sound from the speaker, which is amplified and the sound comes out of the speaker, which is picked up by the transducer... etc., etc., etc.. So it could be a mic and a PA speaker, both connected to the same PA. Or it could be a guitar amp speaker and the guitar's pickups. What you are describing is two transducers together (mic and pickups), which cannot cause feedback.
So what I am thinking is it's the mic and a speaker. Do you have a monitor speaker in font of you? What's probably happening is the sound from the monitor is being reflected off the guitar (which is a mostly flat surface) directly on to the mic (it works pretty much like light bouncing off a mirror). So you'll find if you move the monitor slightly off to one side, so it's at more of an angle, the problem will go away.
;D That leap of realising that the guitar and mic were not only electrically connected, but also probably acoustically was the "Eureka moment". It's the same kind of thing as when your PA is on the verge of feedback and you step up close to the mic and the mic feeds back - what's happening is your head is bouncing some of the monitor sound towards the mic, tipping the system over the edge.
