Microsoft has identified a condition where Free/Busy lookups from On-Premises to O365 in a hybrid configuration may fail.
This problem occurs because of a known issue that affects OAuth connectivity in Exchange Sever 2016 CU8.
To work around this issue, create personal archive mailboxes for each cloud mailbox.
This problem is scheduled to be fixed in Microsoft Exchange Server 2016 Cumulative Update 9 (CU9). For a supported fix for CU8, contact Microsoft Support.