It's my dad's ATV and like the title says it doesn't downshift very well. What could be the problem with that?

 

What exactly is it doing?

Is the dash flashing?

 

Nothing flashing on the dash.
Say your cruising down the trail and then get into a little muddy spot it's like somwone throws out an anchor, tranny starts to bind and engine bogs. Giving it more gas doesn't help. You have to stop so tranny shifts into a lower gear