I have no experience with gluten free, but a great deal of experience with bread.
a few recommendations...
your recipe is in the ballpark of 50% hydration. That is a really dry bread to begin with, and probably one of the main sources of your problem. Try more hydration as a first priority. You could also try more hygroscopic ingredients, different flour types, other moisture holding ingredients. I make a seeded "alpine baguette" where the seeds are soaked overnight, and the soaked seeds keep the baguette fresh for much longer keeping moisture supplied to the crumb. Soak the flour well, try an autolyse, I've even heard of people heating the water for rice flour to saturate it. There are probably techniques from conventional breadbaking that would help you get a more moist, slower staling gluten free bread. I think from your formula you are baking an underhydrated bread, and the rice is not fully hydrated up front, so it is staling quickly as the rice continues to saturate itself drawing water from the crumb after baking.
apparently there is a gluten free bread person named Hagman, see this thread as somewhere to start.
gluten free Hamelman | The Fresh Loaf
most gluten free breads I see use a wider variety of flours. I would suggest you find some on the market in health food stores or wherever, and see what the ingredient list is, and try to go from there also.
Now when you get a good one, I'd like the recipe!