I should add that like any "rule of thumb" there are always exceptions. For contemporary mics using modern materials, leaving a mic powered up will cause no harm. The exceptions are vintage vacuum tube condenser mics with PVC diaphragms. Early vacuum tube mics made by Neumann (U47, U-67 and others) and AKG (C 12 and M 251) originally used cast PVC diaphragms.
Those diaphragms could be damaged by the excessive heat produced by the vacuum tube and its related circuitry (which consume much more power than a contemporary phantom powered, solid state mic). Those early condenser mics benefited from being shut off when not in use. Also, because of the heat produced by the vacuum tubes, the prefered mounting was/is hanging the mic "upside- down" with the grill (and diaphragm(s) at the lowest position, so the tube-produced heat rose away from the "business-end" of the mic.
With the change from PVC or MCF plastics to the more stable polyester (Mylar) diaphragms now commonly used in LDC's, and the use of much lower power dissipation electronics, diaphragm heat aging is not considered to be a problem anymore.