Where the files are saved (Network Drive/ System HDD/ Shared Folder on System /External HDD)?
Does resetting InDesign Preferences (https://helpx.adobe.com/in/indesign/using/setting-preferences.html) help to resolve the issue? Please note that resetting preferences will remove all the custom settings and Illustrator will launch with default settings. You can also take a backup of the folders in case you want to. Location is mentioned in the article.