Note we are on v4.2.12 but your Affected Versions list doesn't show that so I have marked it as v4.2.11

In Edit mode I have used the Insert Tasklist on the Wiki toolbar
Then in view mode I create a new Task - AOK

If I now delete my name in the Assignee box and search for another user with the single man icon and select him, it shows his new user name

If I then hover over the top line, the save icon appears which I click - at least I click on it but I don't know if it has done anything (why isn't that icon popping up automatic and there all the time when any change is made??)

I click the save button.

Close my browser, reopen and it still shows me as the assignee

As a workaround solution, you can edit the page and assignee in the editor.