When HAProxy reloads, it has to re-bind the sockets that it was listening on. Due to a bug in how Linux implements listen port sharing (SO_REUSEPORT), new incoming connections can get dropped for a very brief (~1ms) period while HAProxy reloads. The Github article and the linked Yelp article both go into detail on this.

The tldr is that in Linux right now there is no way to gracefully drain connections from a listening socket. Many programs work around this by passing the socket file descriptor from the old process to the new process, which is, for example, how nginx works.