How long will a sourdough starter last between feedings?
The following is paraphrased from Andrew Whitley's excellent book Bread Matters

Wheat leaven


If you intend to use within 2 days, store the it at ambient temperature
For 2-14 days, store it in the fridge. Optionally refresh it before use.
For longer, refresh then freeze. Refresh again after thawing.


Rye sourdough


0-3 days -- ambient temperature
3-30 days -- fridge, no need to refresh
Longer -- refresh then freeze. Refresh again after thawing.


Whitley describes "constructive neglect". He keeps a rye sourdough in his fridge that's several months old, so that he can demonstrate to students how easily he can take 50g of it and produce a lovely sourdough from it within 16 hours.

It's a great book.