Multilingual MarketPress product pages not shown

I'm developping a multilingual web site (WPML) with Market Press integrated with Appointment+.

My primary language is italian and my secondary language is english.

The store front-end is COMPLETLY UNSTABLE:

Take a look at the product page

You need username= adventurerooms, pw:adventurerooms2014

It correctly appears in the front end. BUT, if I go in the store setting, change the store style, and reload the product page, it shows a page not found.

To make it appear again I must go in the store setting, store url slugs, and saving again the slugs. Sometimes it fixes the problem, sometimes not.

This is blocking my development. Please help, as it appers a bug of some sort with slugs, permalink or something similar.

Kind regards