I remember almost 'losing' the game via not having enough cash for Safari Zone. I have a feeling that was a design error since it can throw you back like ~4 hours if you get stuck there.
The Safari guard will let you in for free if you don't have enough cash (although I believe you'll have a lot less Safari Balls). Aside from the Safari Zone I imagine the other massive wall would be the strength rock puzzles, especially in Victory Road.
Also in theory it would be possible to see the Missingno glitch. That would be a pretty hilarious goal for the twitch players and would certainly make the stream more interesting.
EDIT: Looking at the RNG stream it appears to have captured no pokemon and lacks any poke-balls. Cut, strength and surf are required to finish the game. Charmander can only learn cut and strength which means the RNG requires a pokemon capable of surf.
If the RNG bot keeps failing at battles and doesn't have enough money to buy poke-balls it could reach a massive wall which might have the potential of a lose state. In theory even if the bot runs out of money to spend on poke-balls it could still enter the Safari Zone (for free) and capture pokemon in the grass. It's been a while since I've played pokemon so i'm not sure if there are any grass dwelling pokemon in the Safari Zone capable of learning surf.
DOUBLE EDIT: I suppose it's possible that the RNG would eventually find a fishing rod and capture a water pokemon in the SZ meaning that pokemon does indeed have no potential lose state. Although it's likely to have already captured a bunch of non-surf pokemon which would require a computer transfer which would seem to be another massive wall.