iPhone 6 repeatedly unresponsive

My iPhone becomes unresponsive multiple times a day, only responding to resets. First the WiFi indicator in the menu bar goes from 3 bars to 2, then the sending progress bar atop only iMessages stops at 95%, at which point I can neither receive iMessages nor text messages. Finally any app I open either won't refresh (Twitter, Instagram) or simply crashes (Reminders). Messages at that point (after I've retreated to the home screen, double-tapped and closed Messages) is blank. No 'slide to power off' slider appears, and resetting is the only recourse.