The Angular Velocity of a Rigidbody2D seems to reset to 0 if it is below 0.1 or above -0.1. Is there any way to preserve these minute amounts of rotation?

Exactly what the tile says; I want to have an object rotate very, very slowly but there appears to be a minimum value. Is there a way to override it?

Check your physics2d settings. It should be the “Angular Sleep Tolerance”. The default value is “2”. So once the angular velocity drops below 2 the “Time to Sleep” kicks in and after that time the rigidbody will fall asleep.