Using a starter past it's peak has different implications depending on the amount of starter you're using in the dough.
If the dough calls for a lot of starter then a 'past-peak' starter can weaken the dough considerably (all that prefermented flour subject to excess protease). Also the flavour will be compromised ('off' flavours and high acidity)
If you're using a very small amount of starter then, as Pete showed in his experiment, you're going to deal with different (than expected) fermentation times. Any long ferment of this kind is highly sensitive to the amount/activity of initial leaven.
Ultimately it comes down to familiarity with your starter. Get to know it intimately and don't rely on your starter acting 'by the book'. Given a regular feeding schedule and regardless of provenance, it should eventually stabilize with a predictable cycle and unique balance of bacteria/yeast...which, I guess, is kind of what it's all about in the end.