It takes several hours for healthy yeast cells to remodel their transcriptome and translate the proteins (e.g., enzymes) required to exploit the resources in fresh starter wort. In less than healthy yeast, this so-called "lag phase" takes longer. Several hours more and even up to 2-3 days or longer for yeast in poor shape. Then the yeast cells divide about every 3-4 hours on average, again, assuming they're healthy. If we assume they divide about 5x, we're looking at up to 20 hours. Call it 24 hours, a day. Then we want them to adapt to the resource deficient conditions of the spent wort, before storing them in the fridge. This make the cells much more stress tolerant. Call it another day. So, if we've got healthy yeast, we're looking at at least 3 days for a starter, in my opinion. In your case, where an extended lag phase has occured, experience suggests you let it run for longer, until it shows no signs of activity then another day. If you aim to pitch the yeast directly (without making another starter/feeder), use it within a week, but, again, it depends on the condition of the yeast cells. Some people like to wake up the yeast with a feeder the day before brewing. My preference is to wake them up in the FV wort, which minimises a shock response that risks remodelling the yeast cell chemistry therefore delaying fermentation, especially if the FV wort is significantly different from the feeder wort.
Just a few factors to consider, to whatever level you can be bothered to. I've had slow starters sitting on a worktop for a week or so. Don't be worried about leaving starters for longer. In most cases, it's probably more beneficial than anything. Even in a starter that appears to have finished there is often a lot of cell division still going on, just at a lower rate.
