1.Does the problem happen to all the site collections or just one specific site collection?
2.Can you check if the current account in your SharePoint Designer is the Office 365 account? If not, please switch to the correct Office 365 account and try again.
3.If the account is correct and the problem persists, could you try the following method to reinstall the SharePoint Designer and check the result?
Step 1: Uninstall all versions of SharePoint Designer on workstation.
Step 2: Clear cache (This is only applicable if the SharePoint Desinger is not a fresh install)
a) On the local computer, browse to the following folder:
C:\Users\<username>\AppData\Local\Microsoft\WebsiteCache
b) Delete all the files and folders that are present.
c) On the local computer, browse to the following folder:
C:\Users\<username>\AppData\Roaming\Microsoft\SharePoint Designer\ProxyAssemblyCache
d) Delete all the files and folders that are present.
e) On the local computer, browse to the following folder:
C:\Users\<username>\AppData\Roaming\Microsoft\Web Server Extensions\Cache
f) Delete all the files and folders that are present.
Step 3: Reinstall Microsoft SharePoint Designer 2013
By the way, there is no option in Office 365 to enable the SharePoint Designer permissions, there is only an option in Office 365 to choose install or not install SharePoint Designer from Office 365 Software page.
There is no new Sharepoint Designer after version 2013, you can download it here