Hey, this is Beda, I'll help you with this.
I personally debugged this problem that Nigel referred to as "known", and on the duplicate, I received of your site, I see the exact same issue as I discovered back then, which is a mere cosmetics issue.
On your site, I see something completely different - results change, and that is not what is expected even considering the BUG I already know of.
However, on the Site's Duplicate, I cannot see the issue as it is on your site, but this may as well be due to the fact that the duplicate seems to be a somewhat simplified version of your site.
First, I'd like to ask you if you can perform a few tests in settings.
- Activate "Filtrage de langues pour les opérations AJAX" in WPML > Languages
- Make sure your View's Query is not corrupt, as on the duplicate I received, I saw that some (category) custom filters where not added to the Query filter, hence broken, hence I removed them and re-saved the entire View.
Then, if you have the chance, please check this issue with no other plugins but Toolset and WPML.
Please as well ensure that your Theme is updated, and not customized, for these tests.
If all this does not help, please can you grant me access to the site where I could make changes?
This will require a test site, or the very least, a very good backup of the live site - although it would be safer to work on staging site.
I believe this should be replicable locally but I cannot spot how.
Eventually, I can see the missing part on your site once I log in, or I can fix it right there.