Problems with embedded spreadsheet and the data copied from the same in to the document in which it is embedded

I embedded an Excel spreadsheet as an icon in a Word document so that the spreadsheet can be carried and maintained along with the document. That works perfectly fine. (additional information: this document always has change tracking enabled.)

I double click the spreadsheet, copy the required cells and then go in to my Word document and right click at the location where I want to paste it. I select "Link & Keep Source Formatting" option. The cells get copied just as I expected. (Well, not exactly, the last column was wide enough to go out of the page but then I right click on one of the cells and select "Update Link" and then the column restores to its original size from the spreadsheet.)

I save the document, close it, move it to another folder and then I start getting various problems:

EDIT: I tried with a test document and spreadsheet and didn't moved it to a different folder and I see the same problems. Thus nothing to do with moving the files.

1. I right click on one of the cells I copied from the embedded spreadsheet but I do not see the "Update Link" and "Linked Worksheet Object" menu options rather I see the "Object" menu option. That is to say I can no longer update those cells!
2. I tried closing and opening the document multiple times and only once during all the trials I saw the "Update Link" and "Linked Worksheet Object" menu options but on selecting "Update Link" I got the message saying "Objects in this document contain links to files that cannot be found. The linked information will not be updated". That is surprising because the spreadsheet is embedded in the document itself. I can open it too.
3. When I select File >> Edit Links, I can see the links and they look correct too. However, on the context menu of one of the linked cells I do not see the "Update Link" and "Linked Worksheet Object" menu options!
4. Although I wasn't any optimistic about repairing the office would solve this problem, I still tried it.

EDIT: adding steps to reproduce

Steps to reproduce:

1. Create test.docx and test.xlsx files.
2. Fill up couple of cells in test.xlsx.
3. Open test.docx and embed test.xlsx using Insert >> Text >> Object >> Object... >> Create from File, select test.xlsx, select Display as icon and select OK
4. Double click the test.xlsx icon to open the now embedded spreadsheet.
5. Copy the cells that you filled up earlier.
6. Go to test.docx and right click on the line where you wish to paste the cells. Select Paste Options >> Link & Keep Source Formatting. Your cells should now appear in test.docx.
7. Close the embedded spreadsheet and right click on one of the cells' content and note that have two options "Update Link" and "Linked Worksheet Object", press escape to let the context menu go.
8. Close the document and save it when prompted.
9. Open test.docx again and you should get the prompt "This document contains links that may refer to other files. Do you want to update this document with the data from the linked file?". Select yes.
10. Right click on the text of one of the copied cells and note that you see the "Update Link" and "Linked Worksheet Object" options in the context menu. Press escape to let the context menu go. Close the file and repeat steps 9 and 10 a few times to see the behavior is consistent.
11. Right click on the text of one of the copied cells, select Linked Worksheet Object >> Edit link to open the embedded spreadsheet for editing. Don't change anything, simply close the spreadsheet.
12. Right click on the text of one of the copied cells a couple of times and see if you still see "Update Link" and "Linked Worksheet Object" options. After a couple of times it won't.
13. Close the file and reopen it and try again. You won't see those options again.
14. In order to verify the link information, select File >> Edit Links to Files and note that you will see the link and the information is also correct. However, the copied content in the document is not longer linked and you cannot update it. Thus, basically rendering the feature useless.

How can this problem be fixed?