A hotfix has been released for an issue that causes Availability Groups to show as NOT SYNCHRONIZING. The original issue is described in KB #3033492 and in this SQL Server Release Services Team blog post.
The issue was introduced through Cumulative Update #5 for SQL Server 2014 RTM, and through Cumulative Updates #3 and #4 for SQL Server 2012 SP2. As far as I can tell, SQL Server 2012 SP1 is not exposed to this issue, likely because the specific fix in CU3/4 that triggered the issue was not present in the most recent CU for SP1 (and CUs for RTM stopped a long time ago – so if you're still on RTM, here's another reminder to get onto a supported branch, preferably SP2).
If you're using Availability Groups, or are currently at builds >= 11.0.5556 or >= 12.0.2456, I highly recommend applying the appropriate hotfix. You can download it here:
And you can also see my recommendations in the following blog posts: