The older versions of the Grammarly add-in disable Microsoft Word's AutoSave option using the Word’s API. If your cursor is flashing, this means that the Word’s API is running into a problem when trying to disable AutoSave. This issue can be resolved by installing version 6.6.101 and onward. Download the latest version of the Grammarly add-in and follow the instructions of that page to install it.
Have more questions? Submit a request