I'll give my simple input, which is similar to the others but I'll say it this was; you don't need a lot of the tip of the pick to hit the strings when you strum. I use a very thing pick (Dunlop Jazz III) even for strumming. The Jazz III is a very small, thick and rigid pick. Not ideal for strumming. Give me a standard sized/thickness pick and I can't do it. I gotta use this thick little thing. Other picks feel like dinner plates when I use them.

Point here is that I don't drop the pick. That's due to the fact that I am not hitting the string with the with anything more the the tip. You don't need more than the actual tip. If you dig in deeper (as others said), you're actually hitting the string with more of the pick than you need.

Think of it from a physics standpoint; if the pick is hitting the string in the middle of the broad side of the pick, you have a lot of mass trying to pass through the string. The pick ain't gonna give because you have too much body of the pick hitting the string. The string ain't gonna give because it is essentially a tension cable and it's job is to maintain its rigidity. One strong force against another because there is too much amss of the pick hitting the string.

Solution? Tip of the pick. The is just enough mass of the pick to strick and move the string but not so much that as you're hand moves past the string(s) that the string won't 'let go' of the pick.

Or I coulda said it this way; sometimes I strum without a pick and just use the end of my finger. I'm only gonna hit the string with the tip of my nail and not above the first knuckle (ouch!)..you could see how that would go if I was hitting above the first knuckle. Same with a pick.