Link: https://community.office365.com/en-us/f/158/t/286208

Several factors may lead to the issue when the Office 365 users don’t receive any confirmation after you successfully schedule a meeting or an appointment for an on-premises room mailbox in either Outlook client or Outlook Web App in Office 365. To solve it, please check the following settings:

  1. If your on-premises room mailboxes are not hosted on Exchange 2010 or 2013, please move the room mailboxes to Exchange server 2010/2013 mailbox server first.
  2. Check if the room mailboxes are set to automatically accept the booking requests.
  3. Also, once the room mailboxes are hosted on Exchange server 2010/2013 mailbox server, please set the ProcessExternalMeetingMessages parameter to True by running the following cmdlet on the on-premises Exchange server:

Set-CalendarProcessing ”<Room Name>”  –ProcessExternalMeetingMessages $True

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1. All on premise mailboxes are on Exchange 2010

2. All room mailboxes are set to automatically accept the booking requests

3. I checked the ProcessExternalMeetingMessages on all of the rooms and it was set to $false. I set them to true and then tried booking a room twice. I did not receive a response back either time. It was still set as Tentative. I’ll try again later to see if the problem takes some time to propagate through the system.