AlwaysON : Log_Send_Queue_Size is increasing but the log_send_rate keeps decreasing?
Answering my own question, as future readers will benefit from it :

Seems like we might be hitting Longer latency for SQL Server 2012 database when you use Service Broker, database mirroring, and Availability Groups. This is fixed in SQL server 2012 SP2 CU1. The KB 2976982 has a typo(AlawysOn). So if you are searching by AlwaysON, it wont show up.

After the patch was applied, the issue was fixed.