Why do burgers sometimes fall apart on the grill?

In addition to the fat content, making sure the meat is cold while forming can help.

I generally find that you need a binding agent in the pattie to ensure it stays together - either egg or breadcrumbs work well.

I always use a patty press when I make my burgers since it compacts them really well and helps them stick together.

Freezing patties before cooking them keeps them much more solid on the grill until they're cooked enough to hold together and reduces the amount of sticking to the grill.

Try refrigerating the patties uncovered for an hour after forming. This will give the proteins time to cement together and can give seasonings time to meld. Handle gently while cooking as jwiley suggests.

Alternately you could a finer chop or work it with your hands or a mixer. The more it's worked the stickier it gets. But that kind of texture might not be what you are shooting for.

Cheers

Your guess is correct. Sometimes it also sticks to the grill and gets damaged while turning it . You can use a bit of vegetable oil to make the grill surface less sticky.

How long into the process are you turning it over? In my experience I try to only flip the burger once, after the side it is first cooking on is done (you can see browning on the edge of the patty). If you try to flip it too soon before the meat has had a chance to fully cook on one side, the meat won't be done enough on that side to hold the rest of the patty together, and it will fall apart much easier.

Oil isn't going to help keep the beef together, the high saturated fats in the meat should be enough to handle this. I'd suggest either using a spatula large enough to fit under the size of the patty you're making, or letting it cook longer before trying to flip.