There are a few causes for this, in order of most likely to least likely:
1. The notification sounds are turned down or muted.
2. The phone is not in an area with internet service.
3. The phone is connected to a wifi network with a captive internet portal.
4. The carrier does not allow data use during an ongoing phone call.
5. Other data issues.
Check that the volume is turned up on the phone, and on an android the volume inside the app settings is turned up as well.
Ensure there is a data connection, either wifi or mobile data: test by openning a website such as google.com or cnn.com
Also, test that a website such as google.com or cnn.com can be loaded at the same time a call is in progress.
Then, to call Smart Pager support, inside the app, from the info button (circle with i inside), then Call Support. It is hard to troubleshoot this kind of issue without catching it in the act.
Also, to start keeping track of where they are when the issue occurs, as sometimes these issues are hard to pin down if the provider moves between a few hospitals.