It really is a question of playing the board on its merits, working out the mathematical odds, and perhaps using some intuition in the context of the relationship with the banker, but it is quite significant how many times the optimum time to deal is when there are five boxes left:

Correct
The 3 from 8 round is the key round in the Game
You have 1 chance in 56 of taking out the highest 3 (as I proved)
and if memory serves me right 1 in 9 of taking out the top 2.
If you have 3 or more decent amounts - you have to play on!

I'd always look at the board rather than the money on offer to see whether I'd play on, in theory anyway, but I might chicken out when it got past £20k or so!