I have the exact same problem in version up to 3.7.1.
I have a field of type “entries” that not translatable, since the list itself contains its own translations, and whenever I modify the synchronized record in the other site (English), the list clears itself. I have to go back in the primary site (French), put the elements back, and save again for them to reappear.
As shown, multisite is synchronized and the displayMode is taglist. The condition doesn’t work but that’s another issue.
As per your suggestion, @Zmove, if I change the displayMode to relation, the problem goes away and my saving in either site does not affect the values in the features field.
In the first example: Each Prestation can be stored individually for each Realisation and it works toggling between English and French. There is no sync mode, so switching to French did ask if I wanted to created a record, as expected.
In the second example: The records and fields are both synced, so changing the taglist on the English site will update the French site, and vice versa.
I could not see where values are not saved, where they disappear, or any difference between displayMode: relation.
This is tested on v3.7.1.
More detail might be needed here with exact steps for reproducing it. Sometimes the devil is in the details!