Thyme Plants Not Producing Seeds

I cut thyme cuttings from a thyme plant that I winter in the house and plant them in 4" pots. I grow the cuttings indoors and then take them out and put them in the garden in late May. They do very well. My problem is that I have tried on numerous years to have one or two plants go to seed but have been unsuccessful.
I even tried having the long thyme branch that has the small white flowers rub on each other but no seeds.
We have plenty of insects in the garden. I don't know what I am doing wrong. We live in Toronto. So the plants freeze and die and I have to take one or two indoors to propagate for the next year.
It would be of great help if I could let a thyme plant go to seed, harvest the seeds, and plant the seeds instead of cuttings.

You may not be doing anything wrong. Not all varieties of thyme are capable of producing seeds. For example, most of the creeping types, with a few notable exceptions, such as wild thyme, do not produce seeds. Even some of the upright varieties such as silver thyme and golden lemon thyme do not produce seeds in our experience. The vast majority of thyme varieties we sell are grown from cuttings or division only.
The garden thymes – english thyme and french thyme (Thymus vulgaris) – do produce seeds. If you are growing one of these varieties then I wonder if you might have missed the seeds when you looked because the seeds are so tiny. They shatter (fall to the ground) easily so before you know it they are gone.