When you said “Listbox”, did you mean Combobox or SELECT control with Multiple option enabled under the Fields setup?
If so, then you should set Disabled property instead of ReadOnly to true
in Page_Load server event that belongs to the Edit Page, for example:
$this->MyField->Disabled = true;
This will make the MyField field become disabled, and when you save that Edit form, then the values in that field still remains.