I think a lot of people these days get into sewing for the fun of it. They want to make a quilt, or a Christmas stocking, or maybe a new dress. They don't necessarily jump on board because they want to hem pants or sew on a button, but that's a nice side effect of learning the skill. Sometimes there's utilitarian sewing to be done, and this is that. I felt like both an idiot and a genius when I came up with this solution, because I was thrilled I'd solved the problem, but couldn't believe I hadn't thought of it sooner.
This is what my side of the bed used to look like in the morning. This is a pretty thick mattress, but the sheets are supposed to be made for such a thing.
I tried every sort of sheet anchor there is out there to hold those corners down, and even some things that weren't intended for sheets at all. They worked for a while, but eventually they broke, usually on the other side of the bed, where that guy is trying to win a fight in his sleep.
One day it occurred to me, rather than clipping something onto the sheet, I could just sew in a permanent solution. If you've dealt with this problem, let me share how I fixed it.
You'll need 3/4" wide elastic. This is pretty flexible - I think 1/2" or 1" would work as well. Cut a 10" piece for each corner.
With the wrong side up, lay out your sheet corner at the seam. Pin one end of a piece of elastic 7" from the seam.
Repeat with the other end on the opposite side of the seam. Make sure the elastic isn't twisted. I'd recommend pinning it with some safety pins at this point and doing a test run, since all sheets and mattresses are different.
You may have to stretch the elastic on your sheet to do this. Fortunately it doesn't have to be precise to work.
Stitch across the elastic on top of the hem.
Fold the elastic over itself.
Stitch a rectangle over the doubled section, then an X through the center. Mine isn't pretty, but it sure does its job.
Now you just slip that elastic under the corner of the mattress when you put the sheets on, and they stay put.
Even when you're sleeping next to a bear!