why are my Database backups occasionally failing?
I have not solved the problem The problem reamains that bad backups
  are being taken. I am worried that something is wrong with our prod
  server in General or those databases in particular. I am afraid that
  my work around will only hide the problem and that we have a train
  wreck coming down the line.


Yes.  You should be afraid, and proceed on the assumption that your storage solution is not reliable.  So you should immediately ensure that you are landing good backups on a reliable storage device, and proceed with troubleshooting/support of your production database's main storage and/or backup storage solution.