When you or everyone else have 13 big blinds or less.
If the blinds are 20/40 and you lose a big pot and only have 10BB left, you use the push/fold chart even if there are 9 other players with 50+BB. If you double up to 21BB you switch to the middle phase charts. If you treble up you switch back to the early phase charts.
Until a point where I have the charts memorised, you'll see me flipping between them several times in a SNG. I've played some SNGs where the push/fold stage didn't start until half hour after being heads-up, and others where all 10 of us are still there after an hour sitting with less than 13BB each.
When it gets down to the bubble and it's the late stage (<13BB) I pay more attention to how the others are playing. Instead of pushing in the SB with 75s I'm more likely to raise depending on stack sizes. If I'm in the BB and the others have all pushed, I'm likely folding unless I have a strong hand (or I have a medium-strength hand and am the big stack).
My bubble play adjustment is mainly because I single-table and am playing at a room where there are fewer hands per blind level. If I were multi-tabling somewhere where there are more hands played I'd be more inclined to stick completely to the charts. But after playing one table for 90 minutes, I'd rather have something to show for that time than a 'bubble' finish.