There's one more thing I've failed to mention in my first comment on this topic regrading HAProxy in this scenario. One of the complications is that if we have any new config modifications, you can't simply reload the active process if there are any active persistent connections. You end up having an old HAProxy process running indefinitely until the current persistent connections either fail or timeout for some reason.
We no longer have this issue when reloading Nginx as the new incoming requests are gradually sent to the new master process until the old running process is eventually shut down once all the current requests have been completed.