I must say I have changed my mind on this question. Originally, I favored the idea that the Governor ought to be able to run for re-election, but I have come to the Linwood Holton position (which I hope doesn't happen too frequently)that 4 straight years is enough.
Remember, Virginia's Governors have a lot of power. The Governor has over 4,000 appointments, which is more than the President of the United States, and has the ability to make changes to a bill and then sign it. In effect he can re write legislation.
It seems to me that 4 years with that incredible power is enough. But what do you think?