If your Hyper-V replication is failing over a VPN, there are many possibilities. Gateway based anti-virus and IPS systems, slow WAN links, intermittent packet loss and latency can all contribute to the Hyper-V replication failing over a WAN/VPN link.
There is a workaround which is to use a seed replica VHD to a removable disk and ship it to the target replica site where it can be imported. Then the Hyper-V replica needs only to replicated the changes that have occurred since the seed image was created, thereby greatly reducing the time it takes to complete the initial replication process. This link describes step-by-step how to create a seed VHD image to a USB drive and import it into the target server’s Hyper-V replication topology.
One of the interesting things I have found is that if you create a seed image, you can transfer the image over the WAN/VPN to the target server using the Robocopy utility. On a number of occasions, I have been able to successfully copy the seed image over the VPN and avoid having to drive or ship the USB disk to the target site. The image was successfully transferred over the same VPN link where the Hyper-V replication failed its initial replication.
You can try this by following the steps outlined here to seed a replica VHD, then transferring it to the target server using Robocopy, and finally importing it to complete the process. Follow the steps outlined in the prior link with the exception that the image should be moved using Robocopy rather than physically shipped to the target server’s location.