I actually did sleep through a page once... But two minutes later it just went off again because I didn't hit the "snooze" button. It was one of those "FYI pt's blood sugar was 65 but came up to 95 after eating," so I was able to just look at it and fall back asleep. But now I just place the pager close to my head at night.
Typically overnight I set my pager to "annoying" (the page everyone seems to use as their default), which helps ensure I wake up, and then during the day I switch it back to "beep + vibrate," which is FAR less annoying. I used to use just the vibrate alarm, but then patients think you're faking pages since they usually don't hear the vibrating pager. But why people use the default during the day is beyond me--I swear, some pager tones give me flashbacks...