untenable

adjective2

1. •
   Not able to be held or sustained, such as of an opinion or position.

   • The theory of cold fusion was untenable.
2. •
   Unfit for habitation.

   • It is equally plausible to interpret the evidence to imply a life-span extending well into the fifth century, followed by a phase when the building became increasingly shabby and then untenable. — 2007