I just tried updating Openfire to 3.10.1 from 3.9.3. I noticed that connections worked intermittently.
I tested some connection attempts with Pidgin and about 1 in 3 connections would go through instantly. Other connections would either hang immediately after negotiating the TLS connection or even before that. I observed this problem with other clients as well, such as a python-based XMPP bot we're running.
I ended up rolling back to 3.9.3 and the problem went away.
I could not find any error messages or connection errors logged by the server. The sessions page loaded correctly and all the active connections seemed to be listed and have valid information.
Edit: Just to clarify, I am not using LDAP. My server uses the internal authentication mechanism.