You should normally be culturing a new batch of kefir every 24 hours.
Very strong kefir will be extremely tart and sour and will have separated into layers of curds and whey, some of it chunky. The amount of lactic acid in kefir should allow it to remain untainted for up to a month in the fridge. Sometimes a non-pathogenic white mold called 'flower of kefir' will grow on top of stored kefir. It is harmless and can be spooned off the top. Older kefir can have a very harsh smell, but it smells worse than it tastes. I have made some delicious kefir pies with very strong kefir, that was too strong to drink, with the addition of some sweet milk.