Scheduling and managing events using Outlook.com calendar
If your Inbox is only showing replied invitations and not new ones, you should first check Outlook’s automatic processing settings. A rule or setting may be moving or deleting new meeting requests before you see them. Also check your Junk Email, Deleted Items, and any Inbox rules for the missing invitations. If the invitations are showing on Outlook on the web but not in your desktop app, that would point more toward an Outlook sync issue.
If you can, check whether the new invitations appear in Outlook on the web. That should help determine whether the problem is with the mailbox itself or just the Outlook app.