I assume not very well. All the mini kegs I've gotten haven't lasted more than the night but I bet you could get a couple days and that's about it. I could be way off base so someone else might want to chime in as well.
I'm assuming you mean after it is tapped? I've always looked at the minikegs like growlers....once you open 'em, drink 'em.
I opened one last week, and was wondering the same thing, checked their website for some information: http://www.bellsbeer.com/faq/product-faq/