Inline Editing: conflit with HTML Container Cache: sometimes the inline editing does not work if fragment is already cached without inlined editing option

I have a coupled of pages on my "Web" site. Some are validated, others not. I have a guest users in live mode (all pages in the cache) and antoher (root ) in edit mode.

Inine editing is not turned on for the moment.

On one of the page, I turned it on. I can modify some content. When switching to another page (already in the cache I presume), this is becoming impossible to slected and edit inline any content.

If I purse all caches, it works again.