Eventually he will decide it's well-defended enough. 

"Okay, now try tackling it!"

He is suddenly a lot more concerned.

"Keep up the good work, Amadelphous! You can do it!"

They can keep trading blows for a bit. If nothing changes, it looks like the rock is going to win out simply by being better-defended, but it'll be close either way.

"Try and aim for its weak point! It's vulnerable in its front!"

It's not clear how much she's picking up on his instructions.

But her next shot connects, dead-on.

His Roggenrola falls unconscious.

This wasn't supposed to happen! He had a strategy. You aren't supposed to lose if you follow your strategy.

He will pay out some money to the winner (not very much, he's still just a student) and try to figure out where he went wrong.

How is Amadelphous looking?

She seems pretty tired. If she got in another fight like that one she'd almost certainly lose.

Is he allowed to just turn around and go back to the Pokémon Center? No one's told him that's not allowed, but if it isn't he's going to feel really stupid. But it's not like he has a better idea, either, and he's barely made it past the gate.

"Do you want to go back to town and get healed up, or would you rather keep going?"

Chirp chirp!

He's not really sure what he was expecting. 

He can see more people ahead of him in the distance. He calls Amadelphous back to her ball and turns around, heading back towards Nacrene City.

The gate is still stubbornly convinced that it's 2010.

"Did you forget something?" asks the girl he was talking with earlier. 

"I'm here to get Amadelphous healed up. Is that allowed?"

"Yeah, obviously? I just wasn't expecting to see you so soon."

Oh no, is she going to think he's totally inculpable at weird-animal-fighting?

He hands over Amadelphous's ball to the nurse, then takes off as soon as he's gotten her healed.

Most of the people on Route 3 are kids, and Audino have a fair amount of endurance. If he doesn't mind possibly looking silly and wants to run back to the Pokémon Center every time things start to go wrong, he can make to to Striaton City without Amadelphous ever fainting.

Not in a single day, though. Is he going to travel in the dark, sleep in the Nacrene City Pokémon Center overnight, sleep by the road, or stop running back to Nacrene after every couple fights?

Are there fewer people who want to fight him if he travels in the dark?

Fewer, yes. None, no. Most of the other trainers seem to be going for the roadside camping option, but not all of them.

(He is actually pretty concerned on behalf of the children who are camping alone by the side of the road. If they were teenagers it would be one thing, but several of them look like elementary schoolers.)

If he can't avoid having to fight people by travelling at night, he'll go back to the Pokémon Center in Nacrene. He's planning to leave tomorrow before anyone else can ask him why he kept coming back.

They're mostly assuming it's a weird foreign thing. No one stops him from leaving in the morning. (The girl he was talking to had already left well before he arrived for the evening.)

He will just keep doing this until he gets to Striaton, then.

What sort of weird animals does he encounter?

Depends, is he venturing into the tall grass? What about taking a detour to fight some preschoolers?

...No.