This was an issue a while back with the Nvidia Shield but I believe that was fixed. The problem still exists however with my onn 4K boxes and Tivo Stream 4K boxes.
People are reporting the same issue with their Fire TV devices here:
Not sure if it's audio related but if I change the Audio stream to Spanish (which is just English 2ch) from the primary English track (English 6ch) the number off dropped frames is reduced SIGNIFICANTLY.
As I mentioned in another post, if this issue can't be fixed, can we at least have the ability to change the default audio to the secondary Spanish track instead of the primary English track? This isn't a fix, but is a band-aid for improved video playback.