Avoid alpha texture/material fade with distance

The character model in which has two pieces of mesh in front of the actual model and use a standard shader with rendering mode set in cutout and using alpha textures for the eyes and mouth.

Eyes look fine, however, the mouth tends to disappear/fade with the distance. What can I do to keep showing the mouth? is there a better material settings?

seen from afar: seen from near: I don't really want to modify all my mouth textures to make edges even thicker or it may start looking weird when seen from near...

Thank you in advance