Certified GKH Gardening Expert
Your tree may be in the early stages of decline. This calls for some fertilizing, deep watering and pruning away of dead wood. Here's an article from an Illinois extension service that may help: http://ipm.illinois.edu/diseases/series600/rpd641/. Look for signs of disease - this article will give you some pointers: https://www.gardeningknowhow.com/ornamental/trees/linden/diseases-of-linden-trees.htm
If bare branches continue to appear, I would contact a professional arborist for further treatment of your tree.