The term "text box" is ambiguous. Therefore please describe how you insert such object.

Please attach a small document, which has got such "text box".

System:  HPO Elitebook
Windows 7 Enterprise Service Pack 1 - 64-Bit
Processor Name:	Intel Core i5-4300U
Processor Speed:	1.90 GHz
Memory:	8 GB

Open Office vs 4.1.1

I tried to recreate the issue using a drawn textbox vs an inserted frame.

Drawn Textbox
1. Open Writer
2. Start a clean document
3. Menu: View -> Toolbars -> Drawing.  This will give you a menu bar at the bottom of the app.
4. Click on the "T" for Text.
5. Draw a textbox rectangle on the screen.
6. Typed text "Confirming bugs helps everyone."
7. Click out of textbox somewhere else in document (textbox frame disappears)
8. Select some other text and copy it (CTRL-C)
Test 1
9. Click on textbox.  Does not show text blinking cursor.
10.  Cannot Select text with mouse.  It actually drags the whole textbox.
11 Paste Text (CTRL-V) nothing happens
Test 2
12. Click outside textbox so it loses focus.
13.  Click on textbox.
14.  Start typing, text blinking cursor appears at end of textbox text and typed text appears.
15.  Paste Text (CTRL-V) text pastes at the end line
Test 3
16. Click outside textbox so it loses focus.
17. Double click on the text that you just typed in the textbox. I could start editing (cut/paste text, selection, etc...)

Insert Frame
1. Open Writer
2. Start a clean document
3. Insert Frame.  Menu:  Insert -> Frame
3.1 Clicked OK on frame dialog
3.2 Expand text frame grid on document
4. Typed text "Confirming bugs helps everyone."
5. Mouse clicked outside of the text frame somewhere on document to make it lose focus.
6. Clicked back inside text frame.  Instantly saw flashing cursor.
7. I could start editing (cut/paste text, selection, etc...)


I then tested this same functionality in MS Word 2010

Drawn Textbox
1. Open Word 2010
2. Start new document
3. Menu:  Insert -> Text Box -> Draw Textbox
4. Draw textbox on doc
5. Cursor is blinking and I was able to type "Confirming bugs helps everyone."
6. Click back inside text box, blinking cursor is immediately shown.
7. I could start editing (cut/paste text, selection, etc...)


Insert Frame
1. Open Word 2010
2. Start new document
3. Insert Frame (Used instructions from (http://www.extendoffice.com/documents/word/733-word-insert-frame.html#a2)
4. Cursor is blinking and I was able to type "Confirming bugs helps everyone."
5. Clicked outside the frame so it lost focus.
6. Clicked back on frame, text cursor immediately appeared
7. I could start editing (cut/paste text, selection, etc...)

Overall, looks like the Writer Drawn Textbox does not function the same as MS Word Drawn Textbox and either applications' Insert Frame functionality.

Created attachment 85848 [details]
TextBoxDisappears gif

Configuration:
Attempt to replicate 1: Windows 7x64 SP1, OO Writer 4.0.0, OO Writer 4.1.3
Attempt to replicate 2: Windows 10, OO Write 4.1.3
Follow-up tests: Windows 10, OO Write 4.1.3, Microsoft Office 2016 


Roland’s comment “This bug is from the beginning of the 4.1.1 Version.” lead me to believe that testing on a version prior to 4.1.1 there is possibility to see a difference in behaviour.
For this I have used test steps provided by Rob, in his comment above, for both “Draw Textbox” and “Insert Frame”. The results after testing on 4.0.0 and 4.1.3 are the same with the ones described by Rob.


After doing some follow-up tests I can also add the following results, that, I think, might be close to Rob’s concern and also a few of my concerns.


Results after follow-up tests:


Result 1: The text box is disappearing before inserting text, if you click on it or outside it
Steps to reproduce:
1.1. Draw a text box and select text from the above paragraph to insert in it
1.2. Click on where the text box appeared before clicking outside > the text box has disappeared
1.3. Draw a new text box and click inside it > the text box disappears
See attached gif: TextBoxDisappears
> In order to avoid the text box to disappear you need to type text or use CTRL+V to paste text in it.


Result 2: It is not possible to Paste in a text box from the context menu (Right Click > Paste)
Steps to reproduce:
2.1. Create a text box and add some text in it
2.2. Select some text from inside the text box and right click > Copy
2.3. Hit the Enter button and on the new line right click > The Paste option is missing
> This is inconsistent with the Context menu used outside text boxes. On those context menus the Paste option exists. Inside text boxes you can Paste only using CTRL+V.


Result 3: It is not intuitive how to start inserting text in a frame
Steps to reproduce:
3.1. Insert Frame from Insert > Frame > Ok
3.2. Click inside it > Frame options menu is displayed
3.3. Click outside the frame to lose focus and click back inside the frame > the blinking cursor is displayed
> Another way to start inserting text is if, instead of step #3.2. you start to type directly - this will enable the cursor


Result 4: Text boxes created in an MS Word 2016 are not displayed in OO Writer 
Steps to reproduce:
4.1. Use attached document (TextBoxAndFrame.docx) to open with OO Writer 4.1.3 > the text box is not displayed and neither the text inside it
> The .docx document was created with MS Office 2016 and it contains one frame and one text box
> Neither the frame nor the text box are displayed in OO Writer when using a similar document, created with MS Office 2007


Conclusion:
Using text boxes and frames inside OO Writer is not very intuitive when it comes to adding or editing text inside it. On top of that, text boxes and frames created in MS Office are not supported in OO Writer.

Created attachment 85849 [details]
InsertTextInFrame gif

Created attachment 85850 [details]
TextBoxAndFrame in MS Office 2016