When would we likely see an increase in the CPF Life payout age? It seems inevitable. And to what age can we expect this to be the case?

I would guess it's highly correlated with the average mortality rate of Singapore. I would estimate the payout age would be our country average lifespan + 20years. If I recall correctly before CPF Life starts, the Minimum Retirement Sum would have last CPF members about 20years upon retire. Thereafter no more payout.
And, yup, currently average lifespan of Singapore about 85 years old. So 65 layout age is just nice.
Perhaps when the average lifespan of Singapore goes up to 90, then perhaps, the payout age will increase to 70.

This is a difficult question to answer as the government will have to balance both political considerations and feasibility. From my personal opinion, as age expectancy improvements slows down, the payout age will also change accordingly. Perhaps a gradual increase of 1 year, for every 5 year period, which will be capped at 70 years old from the current 65 years old, would be my best guess. This is really just a very rough estimate, and I'm sure a thorough feasibility study will be conducted before the payout age will increase.