Many years ago in my early days of shepherding, I used to leave the tup with the flock all year too, until one year I had lambs born in October! .
I couldn't believe it as the only time the tup had access to the ewe in question was for a couple of days after she had given birth. I saw him smelling her but I thought he was confused by her birth hormones. After he started being coarse with her lambs I decided he had to be moved out and he stayed out all summer. In late September I thought the ewe had got so fat that if I didn't know better I would have said she was pregnant - call me stupid, because I even thought she was walking and behaving like a pregnant ewe, and still the penny didn't drop!
On October 3rd a neighbour knocked on the door and said, 'did you know you have two black lambs in the field?'
I thought she must be looking at a molehill, but went out to look anyway and, sure enough, there they were.
Now I don't believe in a specific season and manage my tup accordingly. It's probably a long shot but it can happen.