Autodesk has changed the behavior of the default text editing command in AutoCAD 2015.
In previous versions, it was possible to edit one text and immediately go to editing of another text (next selected). This is no more possible in AutoCAD 2015. After you edit one text object, the command terminates.
This changed behavior is caused by differences between the old command DDEDIT and the newly used command TEXTEDIT.
You can avoid this quite simply. In the CUI dialog box, change the command macro for the option „Double click actions“ > „Text“ > „Text Edit“. Write the following command to the field „Macro“ on the right-hand side:
(sans the quotes) instead of the existing: