SQL Server 2008 R2 : Unexpected timeout with SQL Agent Job/powershell
Here is what I use in my PowerShell scripts that I experience issues for timeout. 

Invoke-SQLcmd $SQL -QueryTimeout 65535 -ConnectionTimeout 0


Reference: 
https://docs.microsoft.com/en-us/powershell/module/sqlserver/invoke-sqlcmd?view=sqlserver-ps