The difference between "忍受不住" and "忍受不了"
忍受 = to endure/ to stand (put up with)


Your question is about the difference between two particles '住' and '了'; It also involve the usage of a potential particles '得'  (see How to determine the part of speech tags of words succeeding 不 like these?)


  住 as a particles denotes a verb is in a continuous state: 
  
  忍受住 = to endure (continuously)
  
  忍受得住 = able to endure (continuously)
  
  忍受不住 = unable to endure (continuously)


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  了 as a particles denotes a verb is completed
  
  忍受了 = have endured
  
  忍受得了 = able to endure (successfully)
  
  忍受不了 = unable to endure (successfully)