We study the Keller-Segel system in the plane with an initial condition with sufficient decay and critical mass 8p. We find a function u0 with mass 8p such that for any initial condition sufficiently close to u0 and mass 8p, the solution is globally defined and blows up in infinite time. This proves the non-radial stability of the infinite-time blow up for some initial conditions, answering a question by Ghoul and Masmoudi (2018). This is joint work with Manuel del Pino (U. of Bath), Jean Dolbeault (U. Paris Dauphine), Monica Musso (U. of Bath) and Juncheng Wei (UBC).