what makes my meatballs fall apart when I simmer them in sauce?

Can you share more about the recipe you are using? In general, this is cause by a lack of a binder. Many recipes use eggs to bind the meat, you might want to add or increase the amount of egg. Breadcrumbs also act as a binder, but too much breadcrumb can also cause them to crumble. Here's a basic recipe: http://www.foodista.com/recipe/XDJWP2CS/basic-meatballs

Excellent answer! The protein in the eggs as well as the starch in the bread crumbs provides an effective binding agent. Also, you must make sure that the mixture is properly kneaded before making the meat balls. Then you should gently sautee them before your intended use. You should not have a problem again if this procedure is used. PB (Mycochef)

I agree with the egg and bread crumbs. I also add grated Parmesan cheese. It not only give it flavor but also acts as a binder.

i use 3 eggs per pound of meat. also.... once you put the meatballs in the sauce you have to be very, very gentle when you stir them or they will fall apart. just barely move them at all once they're in the pot. you may be stirring them too aggressively.

The eggs and bread crumbs are a must. However you can cut down on the eggs a little ( I find too much egg makes the meatball rubbery) and bake them off in the oven until the outside crusts up a bit (about 20 min) ir sear them in a skillet before you drop them into the sauce, it will help them hold together a bit better

Rather than breadcrumb how about making a panade, using stale bread with milk? This has been the best trick for making my meatballs tender. I use an egg or two to bind the meat and then sear the meatballs off to caramelize them, which gives extra flavor and dimension to my sauce. Here i my recipe for spaghetti and meatballs. http://www.foodierelations.com/2011/01/spaghetti-and-meatballs.html