Is stabilizer needed late in the year for shutdown?

[Spensar]

waterbear, in Nova Scotia Pibster is likely winterizing and closing the pool within the next month. The cost of stabilizer may be greater than the chlorine to get to shut down. Though there could be benefit in helping to retain the chlorine level after closed, and until the water starts to freeze up.

Would this change the stabilizer recommendation for this circumstance?

[waterbear]

I would really want to see the test resutls first. Even for a month it might be a good idea. It might be worthwhile to chlorinate with dichlor instead of bleach since it will add 9 ppm CYA for every 10 ppm chlorine added BUT without knowing the current stabilizer level and the daily FC loss and if there is any CC it really is impossible to say. There could also be something esle going on such as a nascent algae bloom and that would not be good right before closing.
Finally:

PH and alkalinity are fine

are not test results that give us any useful info.