The key is to not overfill the damned tortilla. The top and bottom "flaps" should be able to fold down to the middle of the ingredients. If they can't at least fold down that far your burrito will deconstruct itself mid-meal. I like to create a polar burrito where the bottom flap reaches past the ingredient center to give more surface to attach to the side flaps. I'm ok if the top flap isn't super secure as it's eaten in the first two bites.

An inedible wrap should not be the only thing keeping the burrito together. Biting the burrito will cause it to leak inside that wrap then it makes a mess. Overstuffing a burrito might give you more food but at the expense of the burrito being an entirely self contained unit of perfection.

Also if you've got store bought tortillas stick a damp paper towel between them and microwave them for 10-20 seconds on a plate. You'll get a partial steam and they'll be more pliable and you'll get an easier wrapping experience and a superior burrito over a tortilla fresh out of the package.