You may be able to add a piece of elastic across the bottom of the corners that will slide under the mattress and help keep it in place.
You can buy elastic strips that attach to the bottom of the fitted sheet....
Sheet straps or sheet suspenders work great! Available at WalMart, Amazon, Bed Bath and Beyond, etc.
On Amazon you can buy “ Hold-up adjustable sheet mattress corner straps with patented grippers”. I use these on all my beds. They work fantastic and they last, I have had mine for over five years. I use them on all four corners of the fitted sheet and I also use two of them on the end of the top sheet. I connect the straps to the the fitted sheet on the side, my husband was always pulling the top sheet out from the end of the bed. I guarantee these are the best on the market .
These straps work well for securing sheets to a bed: https://amzn.to/2Q5w9Yr
Hope this Helps! Jeremy - https://do-daddy.com