Mahbubeh,
Our subscriptions are for 6 months at a time. The v3.4 release is more than two years old, but would have functioned fine until about October of last year. Facebook makes constant changes on their end and we are always updating and improving JFBConnect to make sure it works with regardless of changes to Facebook or Joomla.
If you need the login functionality, you'd need to install the v4.3.4 release, which is the last version we released for Joomla 1.5. That is still available to active subscribers. Since your subscription expired a long time ago, you would need to subscribe again to have access to that release.
We do not provide installation services for our extensions, but do provide great support in case you run into issues with a current release.
I hope that helps,
Alex