For third-person subjects, use the singular verb form (e.g. "doesn't") if the subject itself is singular (e.g. "memory", "bed") and the plural verb form (e.g. "don't") if the subject is plural (e.g. "memories", "beds"). It doesn't make any difference if the subject is qualified by a possessive pronoun (or which one).
... if the/his/my/their/etc. memory doesn't return ...