When you perform kidney transplants, stop dializarte and fistula is not used. And although the transplant work properly is not indicated close the arteriovenous fistula, unless it gives you problems such as:

A major expansion to bother too
Cause circulatory problems
When overload the heart because the fistula has great size.

Doctors usually try to keep the fistula for hemodialysis facilitate implementation if necessary.

My personal experience was: the first was stopped herself without feeling just a year of my first transplant. And second, with my current grafting, was operated for 16 years without any hassle.
Then suddenly, I had a fistula thrombosis due to insufficient flow and lack of use, which made completely stopped. DVT is quite common and it is not possible to prevent it as the root cause of it is the lack of use.
The reasons why a fistula can thrombosed after transplantation may be:

Lack of use and
Increase in blood viscosity due to increased hematocrit and steroids (hyperlipidemia)

My advice is to take care fistula like when performing hemodialysis, in order to keep functioning in case there was rejection or some other complication that hemodialysis become necessary. In addition, any discomfort you observe, or warmth or redness in the area, go to the hospital immediately.