The event log will generally tell you what product caused the self repair.

UPDATE: See this answer for more information on matching product code to product name: How can I find the product GUID of an installed MSI setup?
See this answer for details on various tools you can use to deal with stuck installations (and explanation of why the original MSI file may be needed to uninstall): Why does MSI require the original .msi file to proceed with an uninstall?
Below you will find the original suggested procedure (I would prefer the information in the above link):
To find information about this product, try this procedure:
- In the image above the GUID for the product that caused the repair is marked. Copy this GUID and open regedit.exe
- Navigate to:
HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\Uninstall
- Search for the GUID you found in the event log
- If you find a match, check the details that show up in the right pane as illustrated below (the images don't match, they are for different products but the concept should be clear):

- Try to run the Uninstall from the add/remove programs applet and see if the uninstall completes.
- If the uninstall completes you might be done,
but if it fails to uninstall the normal procedure is to use the MSICUU2 tool and erase the MSI from its internal database (deprecated tool). I suppose you may have removed a different product that didn't cause the repair?