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Recent studies have suggested that the BitTorrent's rarest-first protocol, owing to its work-conserving nature, can become unstable in the presence of non-persistent users. Consequently, in any stable protocol, many peers are at some point endogenously forced to hold off their file-download activity. In this work, we propose a tunable piece-selection policy that minimizes this (undesirable) requisite by combining the (work-conserving) rarest-first protocol with only an appropriate share of the (non-work conserving) mode-suppression protocol. We refer to this policy as "Rarest-First with Probabilistic Mode-Suppression" or simply RFwPMS. We study RFwPMS under a stochastic model of the BitTorrent network that is general enough to capture multiple swarms of non-persistent users - each swarm having its own altruistic preferences that may or may not overlap with those of other swarms. Using a Lyapunov drift analysis, we show that RFwPMS is provably stable for all kinds of inter-swarm behaviors, and that the use of rarest-first instead of random-selection is indeed more justified. Our numerical results suggest that RFwPMS is scalable in the general multi-swarm setting and offers better performance than the existing stabilizing schemes like mode-suppression.