I strongly recommend not to do that as the token is needed to ensure that the request was made from your page and not from the third party resource.
I am not sure, but probably this can help. Try to modify JS code in /media/com_competition/js/competition.js on line 83:
data: data,
onSuccess: function(response, xhr) {
Change it to:
data: data,
method: 'POST',
onSuccess: function(response, xhr) {
After that rename the file competition.min.js that is located in /media/com_competition/js/ to competition-test.min.js - this will force to load competition.js instead of minified version.
Another thing that comes to my mind - the token by itself is located on the page under csrf.token inside this script:
<script type="application/json" class="joomla-script-options new">
I can only imagine that for some reason sometimes it is not loaded, so Joomla cannot read it and send it with the AJAX request.
Best regards,
Dmitrijs