I'm not sure exactly what you mean by "falls," but if you suspect that it's the potatoes' fault, perhaps you are making them too wet. Also, the recipe I've used calls for the addition of an egg to the mashed potatoes which would help with the sturdiness.

I just mean it doesn't stand like it does in pictures. Like in a nice square. I'll try the egg :)

To make the ground beef or lamb base "sturdier," be sure you're not using too much liquid in it (such as broth, tomato sauce or water).
To help your mashed potatoes be their best, don't peel them before cubing and boiling - keeping the skin on while boiling helps prevent water absorption. It's very easy to peel off the skins after. Drain the potatoes, let cool, peel. Then return peeled potatoes to the drained pot over a very low flame, shaking the pot a few times to prevent sticking, just to dry them out a little more. Then pass potatoes through a food mill or potato ricer.
Always heat your milk (ideally whole milk) before adding to the mashed potatoes and use room temp butter.
By the way, I find a Tablespoon or two of A1 or HP Steak Sauce to the meat does wonders for boosting flavor. Just adds a lot of flavor it would be hard to replicate yourself.

Also, I'm thinking be sure there isn't too much milk going in, or the potatoes will definitely be "softer" and collapse more.

I always stir in, after I cook the meat and veggies, 1/3 of a cup of arrowroot starch. It will make it stick together, and offers no taste change. It works!

Are you pulling it out of the pan steaming hot? If so it will never "stand up". But the more important question, is it delicious? If so, who cares if it looks pretty. Shepard's pie is a lovely rustic family meal. Throw it in a big bowl, mix it all up together and enjoy!!!

Jennifer, thanks, that's an interesting tip to know. I've never added a thickener before, so that's why I was wondering if the issue might be too much liquid (maybe broth?) added to the beef/lamb.

Thanks everyone! Great and useful tips!!