If there is no impact to jobload then increase your timeout to 100-200. The errors are expected because your system is undergoing a high load. This was the solution provided by a Microsoft Premier Ticket.

Yeah try saying that to the storage team:-) I don't know if I wouldn't use storage array for anything. The point is that if I am using AG - I should benefit by having two separate stoarage to avoid single point of failure.

Which version of SQL are you on? What is your timeout set at? What is SQLserver waiting on during those errors? DO you see healthy/unhealthy alerts in databases when you receive this error? Are there any job failures during the error? are there any high loads/ETL loads during the time of error? We had a similar problem in our environment during high ETL loads - the Dbs were available but reported unhealthy/ealthy alerts. We simply increased the timeouts to 100/200 since the alerts were acceptable during these high peak loads.