There could be many reasons why you might want to permanently download Movies Anywhere titles.
Perhaps you want to use them on a a variety of devices or upload them to an HTPC for streaming to your big screen...
Regardless of your reasons, you may have discovered that permanently downloading titles from iTunes or Vudu is troublesome, or or even impossible.
However there is a work around using your linked Amazon or Google Play (via YouTube) accounts and PlayOn Cloud.
I have more in depth coverage of PlayOn in this thread - PlayOn Cloud - This Cloud Does Have a Silver Lining
A free option might be one of the many YouTube downloaders; however I have not yet explored this option.