When I compete in the stamina course, about 20% of the time my Pokémon freeze and somehow the game switches out my Pokémon. This happens particularly with the relay run. Finally, does anyone know why is this happening and how to stop it?

dude, it's probably cause your pokemon is worn out & at some point into their exhaustion the game takes control & switches your pokemon for you...the relay race is really 1 of the easier courses to do...

Also, this goes in the "HG/SS Questions Thread" which is one of the "Sticky" topics here & even has a link for it on the top of every page of the forum, use them for HGSS questions please as this is frowned upon here by the higher ups, etc., just giving you the heads up here...

You do switch out your Pokémon when they get tired, right?

You completely misunderstood my question.

I did? I'm pretty sure I read it accurately.

I'm just saying, you know how Stamina events work right? Your Pokémon get tired and have to be switched out. If not, the game will eventually do it for you.

...which is exactly what I said, just in slightly different words...