The Galactic blue supergiant SBW1 with its circumstellar ring nebula represents the best known analog of the progenitor of SN 1987A. High-resolution imaging has shown H-alpha and IR structures arising in an ionized flow that partly fills the rings interior. To constrain the influence of the stellar wind on this structure, we obtained an ultraviolet (UV) spectrum of the central star of SBW1 with the HST Cosmic Origins Spectrograph (COS). The UV spectrum shows none of the typical wind signatures, indicating a very low mass-loss rate. Radiative transfer models suggest an extremely low rate below 10$^{-10}$ Msun/yr, although we find that cooling timescales probably become comparable to or longer than the flow time below 10$^{-8}$ Msun/yr. We therefore adopt this latter value as a conservative upper limit. For the central star, the model yields $T_{rm eff}$=21,000$pm$1000 K, $Lsimeq$5$times$10$^4$ $L_{odot}$, and roughly Solar composition except for enhanced N abundance. SBW1s very low mass-loss rate may hinder the winds ability to shape the surrounding nebula. The very low mass-loss rate also impairs the winds ability to shed angular momentum; the spin-down timescale for magnetic breaking is more than 500 times longer than the age of the ring. This, combined with the stars slow rotation rate, constrain merger scenarios to form ring nebulae. The mass-loss rate is at least 10 times lower than expected from mass-loss recipes, without any account of clumping. The physical explanation for why SBW1s wind is so weak presents an interesting mystery.
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