The brightest ultraluminous X-ray source currently known, HLX-1, has been observed to undergo five outburst cycles. The periodicity of these outbursts, and their high inferred maximum accretion rates of ∼few×10−4M⊙yr−1, naturally suggest Roche lobe overflow at the pericenter of an eccentric orbit. It is, however, difficult for the Roche lobe overflow model to explain the apparent trend of decreasing decay times over the different outbursts while the integrated luminosity also drops. Thus if the trend is real rather than simply being a reflection of the complex physics of accretion disks, a different scenario may be necessary. We present a speculative model in which, within the last decade, a high-mass giant star had most of its envelope tidally stripped by the ∼104−5M⊙ black hole in HLX-1, and the remaining core plus low-mass hydrogen envelope now feeds the hole with a strong wind. This model can explain the short decay time of the disk, and could explain the fast decrease in decay time if the wind speed increases with time. A key prediction of this model is that there will be excess line absorption due to the wind; our analysis does in fact find a flux deficit in the ∼0.9−1.1 keV range that is consistent with predictions, albeit at low significance. If this idea is correct, we also expect that within tens of years the bound material from the original disruption will return and will make HLX-1 a persistently bright source.