We study robust revenue maximization in a single-object auction when resale is possible. Our auctioneer has Bayesian beliefs about bidders' independent private values but non-Bayesian uncertainty about the resale opportunities (including possible leakage of private information). Under appropriate regularity assumptions, we show the optimality of a "Vickrey auction with bidder-specific reserve prices" proposed by Ausubel and Cramton (2004), which allocates the object efficiently provided that at least one of the bidders has bid above his reserve price. In this auction, truthful bidding and no resale is an ex post equilibrium for any individually rational resale procedure. We show optimality of this auction for a "worst-case" resale procedure in which the highest-value bidder learns all other bidders' values and has full bargaining power. The proof involves construction of Lagrange multipliers on the incentive constraints representing non-local deviations in which a bidder underbids to lose and then purchases from the auction's winner.