Iphone not syncing calendar with Office 365 (business)

You don't mention the versions on the device and server. but there can be issues for old versions

https://support.microsoft.com/en-us/kb/3064000

Jul 26, 2015 8:20 PM in response to AnySuggestionsWelcome
I was told at an Apple Store today that with IOS 8.3, calendars no longer sycned from Outlook.  I had set up appt. for another problem and I was so surprised, I said to the Apple employee," So Apple decided  to make their devicesno longer sync to one of the largest market share calendars?"  Employee just said, "It's a Microsoft-Apple thing."  He then said there was a way to make it work, but it was so much trouble that no one would want to do it.  
 
I said something like_  I know this wasn't your decision, but doesn't Apple realize that millions of people use Outlook, and that Outlook is often used in the course of these millions of people's employment? 
 
He said something like - consider switching to gmail & use the associated calendar.
 
iPhone 6, iOS 8.3, Outook 2013

Thank you, I had found that article also.  The IOS version is 10.0.0.2, says it's up to date.  I am using Office 365, hosted by AppRiver.

FYI: I added this email account to my android phone and get the same calendar appointments as his IPhone.

So it looks more like a mailbox issue than a device issue. Are events created in OWA synced to Outlook?

Yes, Outlook and OWA look good and are syncing.

Try point 1.12? Or 1.9?
Issue 1.12 - Appointment in Outlook or OWA is missing on iOS device
When a user syncs a mailbox by using an iOS device, the calendar on the device may be missing one or more appointments. These appointments are available when you view the calendar from Outlook or OWA. There may also be duplicate instances of the appointment in the calendar if the appointment is accepted from the device.

For more information, go to the following article in the Microsoft Knowledge Base:

3012590 Instance of calendar appointment is missing or duplicated on ActiveSync client

https://support.microsoft.com/en-us/kb/2563324

Was this account recently added to the phone or has this issue just start happening?

I've had some outlook issues with syncing with the latest iOS.
One simple thing that I've done to fix this issue is to go into Settings > Mail>Accounts> Select the email account>Turn off in your case Calendars. Turn off the phone. turn the phone back on and go back and turn it on and it worked.
 
Now with that being said it hasn't worked all the time, but the ones that it didn't work for were from clients running exchange 2010 or older. And in that case for the mean time I have them running the  Outlook app on their phones.