HTTP is a request-based protocol, there are no "persistant connections" like they are on SQL, SMTP or FTP (where one connection may handle more than one action).
The HTTP Keep-Alive is some kind of persistant connection, but it's limited in various ways.
A client may request Keep-Alive, but neither a intermediate proxy nor the server has to respect this request
Servers usually close Keep-Alive connections very quickly (few seconds), because they're blocking valueable server slots.
LWP's Keep-Alive should do the job, but there are other participants who might not support or like it.