Cuban bread gets stale. And hard like a rock. I've tried putting in
The microwave. Then I wrapped it in a wet paper towel, and put that
In the microwave. No benefit. Still like a rock.

Any suggestions

Yeah, Oneill. The microwave isn't the way to go.

Get a paper bag big enough to fit the bread in. No waxed paper bags. Just a paper bag. Put the bread in the bag. Wet it all down thoroughly. Not to the point that the bag falls apart but just thoroughly enough. Place it in the oven at 250 degrees. When the bag is completely dry, pull it out. The bread should be softened.

How do you store the bread when you bring it home? You should leave the bread in it's wrapper and put it into a sealed/zipped plastic bag. It will keep it soft for a couple of days at least.

Cuban bread gets stale. and hard like a rock. I've tried putting in
the microwave. then I wrapped it in a wet paper towel, and put that
in the microwave. no benefit. still like a rock.

any suggestions
Not really because this is a type of bread that is supposed to be eaten right away and not kept for later, just like French baguette. If you MUST keep it then while it is still soft and fresh put it in the freezer (wrapped very well to avoid freezer burn) to keep until you will eat it. Let it thaw and then wrap in tinfoil and bake until all warm.

Wrap loaves in saran wrap while fresh or warm and then put into zip locking bags, generally keeps about a week, but I go early to get it while it still warm.

In the oven, wrapped in foil, heat at 350 for about l5 minutes.

I had to invent something for this science fair in my school so I invented a bag that the cuban bread goes in that keeps the bread soft but it actually makes the bread softer! Its really simple to use.