The blades should are not need sharpening as they were made for thousands of paper cuts. But those were the older dies. the newer dies don't seem to be the same quality as the older ones. I have some of the first Accuquilt dies and they are much different than the dies of today.
I took the foam off one of my dies that wasn't cutting clean at the corners, the 2 1/2 Inch square multi die. There is no way to sharpen the blades unless removing them from the board. The foam was held in place with a few squiggles of glue, not adhered all over. The die cut perfectly after I took the foam off. But dangerous to pick up and store.
I have a few dies that the foam has torn away from the edge of the board. I reglue it. I noticed one die the foam seems to crumble in one spot, it's one of the newer dies. I saved the foam i took off the square die so I can cut a patch to replace the crumbling part if I want to. So far it hasn't interfered with the cutting. The foam is for safety for fingers and to protect the blade edge, nothing else.