Hi and thank you for your question.
This sounds like the front cylinder is running rich. Anytime a bike starts running worse as it warms up, the first thought to come to mind is it is rich. It is a fact that as an engine warms up, it runs richer.
I would suggest confirming this by pulling the front spark plug out and looking at it after you have experienced the symptoms again. Sadly, that could be the easy part of this equation. The difficult part could be determining what has failed and is causing the symptoms.
My question to you is, who did the rebuild? Also, to eliminate any errors in interpretation, would you be very specific about what was rebuilt, especially saying what parts were replaced with new parts.
It would be a good idea to do a compression test on the engine just to make sure both cylinders have within 10% compression of each other.
Some of the potential problems that could cause this symptom is an improperly set float level, worn jets, float needle and seat wear issues, things such as that. If you intend to dig into the carbs, we are going to just have to go into them and inspect and scrutinize each individual component in the carb and take it from there.
Let me know the answers to those questions and then decide what to do next.
PS, if you have not taken carbs off a Virago before, it is not the easiest job at all. It is difficult and tedious. However, if you are up to the task, I will gladly walk you through it.