  We study the problem of repeatedly auctioning off an item to one of $k$
bidders where: a) bidders have a per-round individual rationality constraint,
b) bidders may leave the mechanism at any point, and c) the bidders' valuations
are adversarially chosen (the prior-free setting). Without these constraints,
the auctioneer can run a second-price auction to "sell the business" and
receive the second highest total value for the entire stream of items. We show
that under these constraints, the auctioneer can attain a constant fraction of
the "sell the business" benchmark, but no more than $2/e$ of this benchmark.
  In the course of doing so, we design mechanisms for a single bidder problem
of independent interest: how should you repeatedly sell an item to a (per-round
IR) buyer with adversarial valuations if you know their total value over all
rounds is $V$ but not how their value changes over time? We demonstrate a
mechanism that achieves revenue $V/e$ and show that this is tight.
