SQL Server AlwaysOn Error_number 35206
These errors mean you had a connection timeout.  The subsequent messages are a result of that.   In a multi-subnet environment, each AG will have an IP address in each subnet and be registered in DNS.  The DNS server returns multiple IP addresses when queried. Only one will be online. SQL tries all the ip address, serially, until connection is established.  The TCP timeout is 21 seconds.  If the first ip is not online, it will wait 21 seconds before it tries the next one. The default connection timeout period for .NET client libraries is 15 seconds.  You can see where that could be a problem. You need to read this article http://blogs.msdn.com/b/alwaysonpro/archive/2014/06/03/connection-timeouts-in-multi-subnet-availability-group.aspx

If you don't have a multi-subnet environment, then I would look at the network logs again and see how long it was taking for your tcp connections.