We have seen this in very specific cases: pressing the “Upload” button after selecting the image to be uploaded, would download the image to the computer instead of doing the actual replacement.
This behaviour is actually a conflict with another plugin: Product Attachment for WooCommerce. Deactivating it will restore the correct functionality of Enable Media Replace.
If you encounter the same issue but don’t have the aforementioned plugin, please deactivate all plugins except Enable Media Replace. Then, activate them one by one until you find which one is the problematic one.