One honors a mitzvah by taking care not to downgrade its status. Therefore, if a mezuzah is proudly fulfilling its mission on a doorway that is fully obligated, some authorities write that one should not remove it to place it on a doorway which is questionably obligated. For example, a mezuzah removed from a doorway fitted with a door should not be placed on a doorway that has no door.
They also write that a mezuzah taken from a door obligated from Torah law should not be “demoted” to a door that is obligated Rabbinically. An example of this would be removing a mezuzah from a home that one owns to be affixed to a door in a rental residence.
However, this practice is not mentioned by the Shulchan Aruch and other classical authorities. Consequently, some authorities suggest that if mezuzot are taken down to be checked or for another reason, returning them to their original door would be praiseworthy but not obligatory.
 Teshuvos V’Hanhagos 1:649. Most authorities maintain that a rental property is obligated Rabbinically, 286:73.
 Agur B’ohalecha 39:38:88.