For anyone having a Mac sleep mode issue with Eddie client then the following workaround will most likely work: Install a torrenting program such as uTorrent (or something else that will provide a continuous and ongoing active connection), find a legal torrent, and start a download. This way your Mac's network interface will not shut off during sleep, for the duration of the download, due to there being a continuous active connection (for best results choose a torrent that has one or two peers and no seeds so that the download will last indefinitely). If there is just a passive connection, such as simply being connected to AirVPN, then the network interface will shut off during sleep. The only time I have a sleep issue now is when I reboot my Mac and forget to restart the torrent download. It is a bit of a pain to manage the issue this way but it does work.
AirVPN tech support advised me of the following issue with Mac which suggests why the above workaround would work: When the Mac is put to sleep the network interface is turned off, so any connection is lost. Also, all the applications are frozen, including OpenVPN. Therefore default gateway and routing table remain the same, even though the connection to the VPN is no more active. Under these circumstances, OS X and macOS are sometimes unable to reset properly the network interfaces at wake up, as you have noticed.