I have had a couple instances of a propeller popping off when the motors were idling. I thought they were fully snapped on. but I apparently not.
But this time it happened in mid-air.

I was at about 75 ft altitude and climbing when the aircraft suddenly started gyrating wildly and plummetting into a ravine. I gave it full-up throttle, which seemed to slow it a bit but then all I could do was watch the screen helplessly as the drone crashed down through the scrub oak, hit the ground and tumbled down into the revine. Then it hopped around for a while, due to the props beating the ground, while I desperately tried to shut down the motors. I finally got a disengaged message and everything went dark.

After a horrific ordeal of climbing up and down the near-vertical canyon wall I found the aircraft.  I had assumed a software issue but it was obvious what had happened. Two propellers were seriously damaged, one motor was wrapped up in a tight spiral of grass, and the other propeller entirely missing. It had popped off at the moment the drone went berzerk. A careful examination of the propeller mount showed no damage. Apparently the prop was not fully snapped into place when I launched. I would have thought if it cleared the ground the propeller would be set to stay. It makes me long for the P3 fail-safe attachment option.

Should I be surprised that it flew for ten or fifteen seconds before jettisoning a propeller? That makes me very uneasy, but you can bet I'll be vigilant about making sure the props are snapped on solidly from now on.

The good news is that I replaced the propellers and finished the job. No damage at all that I can detect, which I think is pretty impressive.

The question is why does it not lock into place every time?  
Was there a fault with the propeller, or a fault with the propeller mount?
I would change the propeller mounts too, just to make sure...

This is a very unusual problem for a P4, there must have been a fault, unless you have worn the props or mount out?

Glad you could finish the job.  I always lift off to about 2 meters and check controls and stability. I feel this post takeoff check takes time, but it makes me feel better about the upcoming flight.

If the prop flies off in less than 30 seconds from take off, then the propeller wasn't secured properly. If the  prop lasts longer than 30 seconds when this occurs, then it's either an issue with the propeller or the motor threads. Out of the latter, a prop issue would occur more often than the motor threads barring a crash. It's good to hear that you were able to finish the shoot.

Glad lady luck was on your side that day. Things could have very well turned out differently.
When I install my props I hold the rotor and try to turn the prop in both directions to be sure it has completely locked.
I read a post somewhere about a pilot who had a prop fly off and he discovered that there was a small piece of the clear plastic [seal] up inside it that prevented it locking.
Check and double check everything......

Thanks for the feedback. I inspected the motor mount with a high-magnification loop and it's perfect, so it may have been the propeller.  I'll never be sure, since it came down in the treetops and I couldn't find it. I ordered a couple of sets of both just to be prepared in the future.

And I will take Aeromirage's advice from now on and twist both ways to make sure I have a lock.

I had a prop come off my P4P once. I had it all set up, started the motors and then a few seconds later tried to take off from on the P4P box. I didn't see the prop go but the bird just basically went sideways and upside down off the side of the box. i eventually found the prop about 30 feet away and there was absolutely no damage to the craft or the prop. Needless to say that I replaced it with a different prop, but honestly there is absolutely no sign of any damage of problems with it
I also always make absolutely certain that the props are on properly

I'd just buy some new props and check the plastic on the motors where the props attach

This just happened to me.  Prop popped off after 6 minutes of fairly rigorous flight.  The motor and hub for the launched prop were in perfect condition.  Unfortunately, my P4P was damaged in the crash.

When you check the props are fit ok, give a little pull whilst turning them so that you do not inadvertently push and twist without knowing, this has happened to me too but on the ground,  so i always pull and twist, feeling for the stop at clockwise and anticlock, thats when i 1st fit them, i do the exact same again prior to AC turn on, takes a bit longer but can also save  your ac too

Happened to me recently too. I must admit I skipped my usual start up checks because I wanted to capture something quickly. However, I flew the drone for about 1m and was at an altitude of about 15m, 100m from the take off point, and then suddenly crash straight down.
You just have to very consciously and specifically make sure that the props have clicked into place. The spring that pushes them up is quite strong and so even spining the props both ways with your hands won't pick up this problem in itself. Holding the motor and twisting the prop both ways will check for it two. Also see picture that shows two props. Props on properly have a bigger gap to the top of the motor than ones not on properly.

Check, check, check.