We'd honestly just recommend upgrading to 3.0.3 so that you get the bugfixes and other improvements in 3.0.1 and 3.0.2.
3.0.0 actually used a different method for fetching the avatar from Facebook. We haven't check if this experiences the same failure to download issue as the 3.0.1 and 3.0.2 versions do. I'm assuming you're running into this problem with that version as well?
If so, let us know. If you really don't want to upgrade to the latest, we can provide you with a code change that will make that one section use the same code to download as the newest releases. For upgrading instructions (basically just install the newest version like you were installing it for the first time, no uninstall necessary), check out our upgrade guide:
www.sourcecoast.com/extensions/jfbconnect/upgrade-guide