OK I made tests on your site and for me there is no conflict with Responsive but with All in one event calendar standard. I left your site as is, downloaded the plugin and reproduced the conflict on my test site.
What is fancy is that the lite (no more maintained) version that you can download from www.ads-software.com does not have this conflict.
Then I started looking at aiec standard files, found the proprietary license (which forbids to reverse engineer the program and so to help you) and no reference to the GPL license which according to people more qualified than me is a violation of the GPL license (https://www.ads-software.com/about/license/) used by WordPress.
Then I googled a bit and found:
https://help.time.ly/customer/portal/questions/458479-how-is-your-license-valid-not-a-violation-of-the-wordpress-
So according to the plugin author 99% of the work is covered by the GPL and only 1% is proprietary, but since he does’nt mention this in the distributed files, I can’t know which files I have the right to reverse engineer and modify…
Well, sorry for the digression about licenses, but I would not appreciate finding my contributions in a proprietary software without my permission
Now the solution: Just comment
return $this->_rewrite->flush_rules();
at the line 126 of the file all-in-one-event-calendar/lib/adapter/class-ai1ec-adapter-query-wordpress.php
Then go to settings->permalinks and click on save changes. It solved the conflict on my test site.
Again a plugin author who does not read the codex https://codex.www.ads-software.com/Function_Reference/flush_rewrite_rules#Usage (second time this evening).