Searching for keepalive on the SOAP::Lite manpage, I found:

$PATCH_HTTP_KEEPALIVE

SOAP::Lite's HTTP Transport module attempts to provide a simple patch to LWP::Protocol to enable HTTP Keep Alive. By default, this patch is turned off, if however you would like to turn on the experimental patch change the constant like so:

  $SOAP::Constants::PATCH_HTTP_KEEPALIVE = 1;