You could use a static class or static Object to connect to the
server, and re-use that when needed. (wrap it all in a static method
for login maybe?) You'd probably need to keep a state variable too, to
record if it's (still) valid.
Do remember that the lifetime of the connection is determined by the
Jira-server, if there hasn't been any activity for some time (30 or 60
minutes?, default time-out) the connection is closed, so your
application should be prepared to re-connect on failure, it doesn't
auto-reconnect like the web-pages do.