My 2005 Big Bear 400 is leaking a small amount of gas from the tube that exits the bottom of the carb area. The ATV runs fine, and the leak seems to be present after it sits up for a while.

Any thoughts on what this might be?

 

needle and seat in carb are worn

 

Yup, totally agree, Yamaha spec for needle/seat seal is about 30psi, so even if you can blow into gas line with float up and not pass air, it will still leak gas, had the same thing happen to my Wolverine, felt like it sealed, but leaked out the tube until I replaced needle and seat. Also check float setting while it is apart.