You aren’t giving us enough information to even speculate the answer. Are these Enterprise grade servers in a datacenter? Are these home made servers with consumer or low grade hardware you’re calling servers? Are they in the same datacenter or do they go out to the Internet? What exists between the hops on the network? Is the latency consistent? What is the quality of both sides of the connection? Fiber? Wi-Fi? Mobile? Satellite?

Does it drop too nothing or just settle into a constant slower speed? What have you tried to trouble shoot? Is it only rsync or do other tests between the hosts show the same behavior?

Give us more and you might get some help. If these hosts are Linux I would start with iperf to do a more scientific test. And report to us some more info.

Maybe I’m misunderstanding the purpose or goal but wouldn’t this be perfect use case for a virtual machine? I’m surprised no one has suggested that. A one off temporary, easily reverted back to pristine with snapshots sounds like exactly what you would want for testing something like this out.