Permafrost, or ground that is continuously frozen for at least two years, contains vast stores of organic soil carbon. Stratospheric aerosol injection (SAI) may prevent tipping points that lead to widespread permafrost thaw and carbon release by cooling surface and soil temperatures, but it is unclear if or when permafrost could stabilize after SAI deployment. Using the ARISE-SAI-1.5 simulations, we show that the rate of permafrost thaw begins to stabilize under SAI, but does not fully stop, likely due to deep permafrost thaw processes that are resistant to surface temperatures changes. SAI does prevent a potential tipping point (talik formation) in almost 2 million km2 of permafrost, most of which is located in permafrost peatlands. Thus, a more aggressive SAI strategy may be required to rapidly stabilize permafrost extent.