Take a look a my question over here How to prevent Safari from stopping downloads?. I would mark as an exact duplicate but it is not the same question, only the same answer. The problem that what is occurring is your computer has to wake up from sleep. "But wait InsomniaX is supposed to prevent it from sleeping!" Yes it is. But it does not seem to work in this case.
Since you do not want specific times for the server to wake and sleep I would suggest these settings.
System Preferences>Energy Saver
Computer Sleep: Never
Put Hard disks to sleep when possible: Unchecked
Wake for WiFi Access: Checked
Then open a new
/Applications/Utilities/Terminal.app and enter the following command:
caffeinate and leave it running.
You can also create a LaunchDaemon so that
caffeinate will start automatically on restart.
P.S. I too use my MacBookPro 2011 as a server. I use it with macOS Server to host websites, file server, VPN, and others. Great use for an old computer.