How to keep sectional pieces from coming apart?

Sounds like there's a few things in play here. First, stop "plopping" on the furniture!!! (I sound like what I used to say to my son - sorry!!!) If ya'all don't stop plopping, you'll break down the springs & there won't be any value left when you want to sell it. Second, you need an area rug that at least goes under the front feet of the sectional. Get a rug grip for a rug to wood application. Thirs, call the furniture store where you bought the sectional & ask for a service tech to come out & inspect the connectors. It's possible that they were installed misaligned. If not, have him connect the pieces securely. If worse comes to worse, you can install your own connectors on the bottom on the frame. They are called "mending plates" & you can get them at Home Depot.