I know you weren't expecting it but in fairness to your dog, now you do know, I wouldn't have an in season bytch in the house, even shut away. To the dog the scent is lingering and pervasive.
As a matter of interest, research was done on fighter pilots who lost their gonads. Apparently the chief determinant on whether or not they would continue to have a normal sex life was whether or not they believed they could...I will try and find the paper.