I believe they don't. Gift tips have no strings attached on either side. It's like employment at will, where either party is free to call it off at any time.
"[E]ither the receiver is tied to that nebulous expectation of production, or they can take a break and risk losing whatever funding they received before and the resulting need to build that up again."
I think it's a matter of telling your story openly and transparently. If people see me working productively for a year and then I blog about how I'm burned out and plan to take a break for a month, I would expect my funders to understand and not totally bail on me. I mean, I could set up visits around the country and have a nice vacation and still keep the story rolling. If I'm finding my living on Gittip I have to have a relationship with my anonymous funders and trust them. The Internet lets us have a relationship with the anonymous crowd.
Gittip wants to make it easier for receivers to tell their story. See:
https://github.com/whit537/www.gittip.com/issues/133
This is really WFP's thread, but I'm interested in seeing your site.