This article is specific to AT&T users in the USA experiencing sending or receiving issues while WiFi is on (caused by the November Security update from AT&T).
Firstly ascertain if the issue only occurs when on WiFi. You can do this by sending yourself a picture (firstly with WiFi on, then again with WiFi off).
If the issue ONLY occurs with WiFi on, the solution is as follows.
Android Settings > System (Advanced) > Developer options (turn ON) > (NETWORKING) Mobile data always active = ON
Note: If those settings are not initially there, you need to "unhide them" as follows, then go back and set them as mentioned above.
Android Settings > About phone > Software Information > keep tapping "Build number" till it says developer mode on. Then locate (search) for Developer options in the settings.