Well, I would have suggested after 24-48 hours to put it in the fridge and take it out before you start to brew to let it come to room temp.
Leaving the starter out for a week won't really hurt them, but it usually finishes fermenting within 24 hours for a starter size, so it doesn't help either.
You should be fine overall, yeast is very resilient. Maybe you could increase the starter size a bit to reactivate the yeast a bit, but not really required.
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