Lawns sodded within the last three years are most susceptible. Overseed the lawn with perennial ryegrass and provide proper care to mask the symptoms. This disease runs its course in a few years. My lawn is littered with short twigs from my maple tree. The leaves are green and the tree appears to be otherwise healthy.
Healthy trees can tolerate the occasional loss of a few twigs.
Squirrels or twig pruners and girdlers could be causing the problem. Squirrels often chew through twigs causing the damage you described. It is almost impossible to keep squirrels out of trees. Twig pruners and girdlers feed inside the twigs weakening the stems. These twigs drop during high winds or heavy rains.