Abstract
It has been argued that the so-called memory-burden effect could cause black holes to become stabilized by the information that they carry, thereby suppressing the rate at which they undergo Hawking evaporation. It has furthermore been suggested that this opens a new mass window, between $10^{4}\,{\rm g} \lesssim M \lesssim 10^{10}\,{\rm g}$, over which primordial black holes could constitute the dark matter of our Universe. We show in this \textit{letter} that this is true only if the transition from the semi-classical phase of a black hole to its memory-burdened phase is practically instantaneous. If this transition is instead more continuous, Hawking evaporation will persist at relevant levels throughout the eras of Big Bang Nucleosynthesis and recombination, leading to stringent constraints which rule out the possibility that black holes lighter than $\sim 4 \times 10^{16}\,{\rm g}$ could make up all or most of the dark matter.