The formation of supermassive black holes is still an outstanding question. In the quasi-star scenario, black hole seeds experience an initial super-Eddington growth, that in less than a million years may leave a $10^4-10^5$ M$_{odot}$ black hole at the centre of a protogalaxy at $z sim 20-10$. Super-Eddington accretion, however, may be accompanied by vigorous mass loss that can limit the amount of mass that reaches the black hole. In this paper, we critically assess the impact of radiative driven winds, launched from the surface of the massive envelopes from which the black hole accretes. Solving the full wind equations coupled with the hydrostatic structure of the envelope, we find mass outflows with rates between a few tens and $10^4$ M$_{odot}$ yr$^{-1}$, mainly powered by advection luminosity within the outflow. We therefore confirm the claim by Dotan, Rossi & Shaviv (2011) that mass losses can severely affect the black hole seed early growth within a quasi-star. In particular, seeds with mass $>10^4$ M$_{odot}$ can only form within mass reservoirs $ gtrsim 10^7$ M$_{odot}$, unless they are refilled at huge rates ($ gtrsim 100$ M$_{odot}$ yr$^{-1}$). This may imply that only very massive halos ($>10^9$ M$_{odot}$) at those redshifts can harbour massive seeds. Contrary to previous claims, these winds are expected to be relatively bright ($10^{44}-10^{47}$ erg s$^{-1}$), blue ($T_{rm eff} sim 8000$ K) objects, that while eluding the Hubble Space Telescope, could be observed by the James Webb Space Telescope.
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