this is an interesting topic for thru hikers on the appalachian trail. they not only don't shower for weeks at a time, but also have periods where their water supply is limited, so even the most basic washing up is restricted.
experienced hikers have noticed that after a few weeks, your body begins to regulate it's own stink. i guess the odor causing bacteria begins to level out. but you still have a kind of musky, nasty odor about you, of which people at your downwind campsite know that you're coming a minute or 2 before you arrive...
in nomine patri, et fili, et spiritus sancti.
Meh nom eh noh...doot dooooo do do do.