The ability to get appointments to show up in one's calendar simply be receiving email invitations is very convenient, requiring no setup steps, and usually works well enough.
However there is one instance wherein this fails, and it's a known issue with Outlook when it comes to processing email invites that specify more than one event.
Specifically, certain (all?) versions Outlook, will ignore all but the first event indicated by an ICS calendar invite email attachment.
This arises as a problem if and when you schedule a series of routine Appointments with your client, and send them a single notification of that series.
Workarounds
There are 2 possible if your client has an Outlook client that fails to register any but the first in such a series:
Recommend that they sync their Outlook calendar.
This can be done from their My Account >> Calendar Sync area, and it a one-time set up that takes about 45 seconds. Syncing in this way means all Appointments of a series will be properly added to your client's calendar.
Manually Send Notification Emails of Individual Appointments
With a few clicks you can manually send an invite email for each of those series Appointments beyond the first one. You do this by clicking the gear wheel icon for the client and going to Settings >> Appointments:
Then click the link 'If you're having trouble, here are some ways to help...':
From here, you'll get more information and the option to send a separate .ICS file for each Appointment:
I suppose a 3rd workaround to this would be to complain about this issue to Outlook. That could ultimately yield the most elegant solution, but is apt to take a while. :)