Consider this scenario:
You have a business that uses SharePoint Online, and you do work for a charitable organization that also uses SharePoint Online. You access these SharePoint Online sites using two Office 365 accounts. At different times, you use the site action Sync to SharePoint Workspace on each site to create a workspace from that site in SharePoint Workspace 2010.
However, you notice that only one workspace synchronizes at any given time, and you receive sync errors for spaces associated with the other account. The workspace associated with your current Office 365 login syncs without error. If you log out with your current Office 365 account, restart your browser, and then log in with the other account, the workspace that synchronizes successfully will change to match the active account.
If you have a browser window open and attempt a manual sync on the workspace that is not synchronizing, SharePoint Workspace does not prompt for credentials and the sync fails. If you close the browser window and then attempt a manual sync, SharePoint Workspace does prompt for credentials.
This behavior is different from using SharePoint workspaces with enterprise servers that use Windows authentication, where you can have workspaces that are individually associated with different domain accounts.