The answer is that nobody is sure.

The idea is either Northumberland refused to move the troops forward because he betrayed Richard III, or alternatively that there was some terrain blocking his coming to Richard III's aid. The problem is that nobody is really sure where Bosworth fields took place and thus exactly where Percy's troops were on that day. So we can't confirm/deny the second theory. But it seems to me to be pretty unlikely that Richard III, an experienced battle commander, would place Northumberland in a position where it could not aid the remainder of his army.

At the same time, I believe Peter Reid noted that there is remarkably little record of the Bosworth for such a pivotal battle. As in there were more contemporary sources written about some inconsequential skirmishes than Bosworth. Therefore unfortunately we -are- left to speculation.

I personally think that Northumberland was pretty much doing the same thing as Stanley, which is to say watching and waiting to see which side is winning before jumping into the fray.