Usually 2-3 days is good enough. If you can't brew for a few weeks, then I would rejuvenate the starter when you are a couple days away from brewing.
Stick your starter in the fridge now, then when you get closer, pour off the liquid but don't disturb the yeast cake, add more wort and stick it back on the stirplate for a couple days. That'll give you nice healthy yeast to pitch on your beer.