According to a view (the Beis Aryeh 289:4) a mezuzah that got damaged while it was up and invalidated, one should keep it up until a new kosher mezuzah is affixed in its place. This is because of the rule of "kavod habrios" (honor to the creatures). That is, since it would be embarrassing to leave the doorway without a mezuzah altogether, therefore, one may keep the invalidated one up until the new one arrives. There is room to back this based on the gemarrah (Sukkah 48b) that states that when the mizbeach was chipped in the corner, the people took salt to fill in the corner so it should appear kosher, (even though that this does not validate the chipped corner of the mizbeach).
The Mezuzos Melachim (Halacha Lemoshe 200) prefers that one should take down the invalid mezuzah even though it will not be immediately replaced. The reasoning is, this is different from the case of mizbeach since here the concern is the individual can be lax about this and not end up replacing it altogether, this is unlike the case of the mizbeach in the Beis Hamikdash where there were many to remind each other to fix the problem as soon as possible.
