Why does someone I shared a form with keeps losing access?

Can you kindly clarify what you do mean by "losing access"?

I have checked the form you shared and can see that it belongs to your sub-user. 

Please note that sub-user accounts do not inherit the previleges of a parent account, so does their forms. If that is the issue you are reporting, please try to drag the form into the shared folder of your account (it will be transferred).