I strip piece often. like other said, use a smaller stitch. The other problem is being careful that you aren't letting pieces drag as you are sewing them together, as that can pull the seams a bit apart. I'm talking about the part that is before the needle and maybe hanging off the front of the machine. if it catches a bit as the machine is feeding, the seam may open up more than you'd like.
But it's really no different than if you are trimming a block down to size after sewing, as all the seams where you trimmed now have the threads cut just like happens with strip piecing. I normally sew with a narrower stitch, probably equates to a 1.8 - 2 on most machines. I go a bit smaller than that for paper piecing.
I have also found that the thinner the thread, the more it will open up. Sometimes I'm using up older 40wt thread and that holds very well, but when I'm using 50wt, it opens up a lot easier. Mosty I've learned to be very careful in handling peices.
I also stay stitch all around a floppy if it's got a lot of pieces on the edge, as when I'm pulling straight on the LA, edges opening up can be a real problem.