Some browser configurations or extensions can actually block cookies entirely from being saved, hence the wording of that message.
That said, I don't think that's the issue here.
I have visited the site that is on your license and I can reproduce the issue you're talking about, but only if I go to the http:// URL of your site.
Your site is accessible from both http://s...com as well as https://s...com.
All is fine if you go to the https:// version.
It is wise to have a single canonical URL of your site. The easiest way to do this is to go to Admin CP > Options > Basic board information and enable the "Enable board URL canonicalization". You will need to make sure your board URL setting is correct too (it should be the https:// version).
Once that is in place, people who visit your site on the http:// version of the URL will be automatically redirected to the https:// version, and the error will not occur.