Please ensure, that extensions.rightlinks.enabled (and extensions.rightlinks.enabled.right + extensions.rightlinks.enabled.left) are "true" in about:config page. You may accidentally disable it using hotkey (F2 by default).

And, may be, extensions.rightlinks.showContextMenuTimeout (500 milliseconds by default) is too small for you, try increase it.

If Right Links still doesn't work, please provide detailed description here:
http://forums.mozillazine.org/viewtopic.php?f=48&t=645809
or here: https://github.com/Infocatcher/Right_Links/issues
And please include information from
Help – Troubleshooting Information
(will open about:support page)