Share Counts Show Zero After I Changed My Site Links
If you change the URL structure of your site from let's say yourwebsite.com/link-to-my-article to yourwebsite.com/blog/link-to-my-article the share counts return zero. That's because social networks like Facebook, Twitter are not able to detect this change. Thus from their perspective it looks like it is a new page / post even though the content is the same. That's why the share count is zero.
Think It Thoroughly Before You Change
There is no way to get the old share count back, so think about it carefully if it is really useful or do you really need to change your site URL structure before you do this. Most times you have more drawbacks than advantages when changing URL structure.
Please note that changing domain would have the same effect on share counts