I think this might be a Firefox thing. Currently to clear the cookie the Continue link, links to #. Very interesting says Firefox, I'll just do nothing.
If you update line 43 in escn-ajax.php to say this:
a href="<?php echo add_query_arg( 'rnd', rand(1,65535) ); ?>" id="escn-continue"><span class="escn-icon continue"></span><?php printf( '%s', 'Continue' ); ?>
Then all should be well again.
This leads to Continue adding a random number as a parameter:
http://www.mysite.co.uk/?rnd=RANDOM_NO
or
http://www.mysite.co.uk/?existing_param=1&rnd=RANDOM_NO
Which will force a refresh of the page and thus allow Continue to Continue!
Nice plugin - if you fix it, and I hope you do, please post response here and I'll change my 'Broken' to 'Working'!
Cheers,
Gerald