Edit pen not available at all times


We’re trying to display a list where the data can be edited by specific users. A pen is available at the top of the list and we usually can edit whatever data we want.
But, it seems there is an issue: the pen appears whenever it wants. We didn’t change anything on the page but depending on the publications, the pen appears or disappears (and we’re on test mode meaning that everyone should be able to edit for now)
Does the number of element loaded on a page have an impact? It seems that when there is only the editable section, it works perfectly. But if there are other elements on the page, it doesn’t work as intended…
A page where it works as expected (we did the same on other pages and it doesn’t work as expected): https://newga360.fifty-five.com/test?recordId=recmipQDPIlrrG4gZ

Is there something we haven’t configured correctly? How come the pen disappears whereas we didn’t change our configuration compared to when the pen appears correctly?

Many thanks for your help.