Got it ! :)
I realized that there was "update" requests for not-working properties,
whereas good ones were doing "insert", which is ok because it's a new
object.
I found a bunch of properties for my particular object id in
"xwikiproperties". After purging them and restarting container, my object
saves successfully.
What I do not understand, is how this could happen ?
I still have to test it for all my input data...