This isn't a BE problem per se, but I only hit it on my BE servers because of the version of SQL installed. Very little definitive information out there in MS land on this and even less on the BE forums (I did a search).
About 6 months ago during routine maintenance on a BE v15 server I noticed that KB2977320, SQL 2008R2 SP2 update fails consistently. I tried a few times, couldn't get it to work, moved on. Its been bugging me ever since. Tried again today, still no good.
Turns out that KB2977320 requires dotNET 3.5 to be installed on Server 2012R2 (almost certainly on other server versions as well). Once I did this the update installed without a hitch.
Link that led me to the solution:
https://social.msdn.microsoft.com/Forums/sqlserver...
Good luck all, hope this helps someone.