Cart lost on some computers not others, not mine

Hi all,
Coming to you as a last resort.
We use Drupal commerce and when a user adds something in his cart, the cart shows as empty.
I cannot reproduce the problem at all on our computers ( tested on FF, IE and Chrome on several computers and Pads...). I only know about it because of customers' feedback and also because we almost don't have any orders anymore (and we have more visitors than before, so not a vonversion rate problem I think).

A user in the general forum made a screenshot of what happens :
https://www.dropbox.com/s/34l48n0o9fuqtpf/Screenshot%20from%202013-05-16...
But I totally cannot reproduce on my computer.
I don't see any error on drupal or my logs.

I already Restored defaults on my shopping cart views + using the "Disable SQL rewriting" option.

I disabled lots and lots of modules, repaired tables. Nothing solved.

Sorry if this is duplicate but i've not found an answer.

Ha, the website : www.boitesetmerveilles.fr
We use Domain Access.

Thanks in advance.