"You may not be able to view these attachments after you close the item". I think that's why you don't see the attachment when you open the item after the save. Outlook knows it's there but won't show it to you.

The only thing I can think of that is even close is an old bug where consecutive dots (...), or an exclamation point (!) in an attachment name, including in the Subject of an attached email, would trigger a warning. But you said you deleted all the attachments before saving, so that doesn't fit.

Security update for Outlook 2010: June 13, 2017

All I've got to offer is writing a VBA macro to examine the MailItem.Attachments property, or use a tool like OutlookSpy to examine the invite. (You can use OutlookSpy free for two weeks)

One other thing to try: Print the invite. Look for an "Attachments" line or icons for embedded attachments.