If you currently use a softphone on your iPhone (or you plan to deploy this kind of service to your enterprise users), you are already aware that this softphone is treated by the iPhone as any other app. The APPS are not all equal, so you might have already experienced missed calls on the softphone (when the phone is locked and screen is black – sleeping) – the app running SIP with your PBX was not simply able to be woken up or it was unable to notify you – the user – that there is an incoming call.
Please be aware the for the next iOS APPLE plans to deploy coming September 2017, they will restrict even more the APPs capabilities to wake -up. Once a cell phone call received or SMS or any other apple native APP is UP, your softphone up will go into background or even in inactive mode. This is because APPLE makes higher efforts to preserve the battery and energy of the iPhone (and the APPLE apps for that matter). They offer the developers (for free for the moment) the possibility of using an API called Apple PUSH Notification Service and pass remote notification to the iOS device through this APPLE infrastructure (Internet access needed).
A necessary step will be to check with your telephony provider if the iOS apps that you have running on your users’ iPhones has ben programmed to use this APPLE PUSH Notification Service.
PS: Here you have a link for the Apple iOS APPS developers best practice recommendation https://developer.apple.com/library/content/documentation/Performance/Conceptual/EnergyGuide-iOS/WorkLessInTheBackground.html#//apple_ref/doc/uid/TP40015243-CH22-SW1