I also had this problem, and I got the following in my exception log:
Integrity constraint violation: 1062 Duplicate entry '706-168-2-60' for key 'PRIMARY''
In the end, I discovered (as stated above) that this is a problem with the product identifier 706 (the first digits before the β-β are the product identifier.
Just opening this product in the Magento administrator and saving it fixed with this product, however, in my case, I also had a problem with the product 707, 708, 709, etc. etc.
What I then discovered is the second set of digits identifying the attribute identifier. I found out what attribute it was by opening any attribute and replacing its identifier in the URL with the one that was in the exception log.
Then I looked for a series of products (in my case from 700 to 800), selected all of them and used "Actions" "Update attributes" in the upper right corner of the "Catalog - Product Management" page.
I changed this attribute for all of them (it was good for me) and the index worked.
If you cannot set this attribute the same way for all of your products, I would suggest mass import to reset for just that.
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