Black Hole Electron

Answering that properly would require a theory of quantum gravity. However, the answer is plausibly never.

Such an evaporation would be a form of electron decay. Under the current understanding of particle physics, electron decay is impossible without violating conservation of charge or mass (as the electron is the lightest of the charged particles). Empirically, we have never detected electron decay, and it does not occur often enough to cause significant problems with our current theories, so it would need to be a very rare process.

Additionally, all electrons are, to the best of our abilities to measure them, equal in energy. This means that a hypothetical evaporation process for electrons must be a quantum event. Specifically, Hawking radiation causes black holes to evaporate by emitting quanta of energy. It is not unreasonable that there exists black holes such that there is no allowable quanta of energy that could be emmitted, so they simply never evaporate. In such a model, you would expect black holes to evaporate down a minimal size (possibly one of many minimal sizes), then stay at that size. This would be consistent with the electron being (one of) such minimal black holes.

It is possible that all elementary particles actually black holes, and are stabilized by the fact that Hawking radiation is a quantized process. When you think about it, this isn't even that different from our current understanding of why particles are relatively stable. Any hypothetical decay path is quantized, and there just aren't that many available things to decay into.