“But it still comes out from time to time.”

Your friend is from the southern part of the U.S. He says that he used to have a strong Southern accent growing up, but he tries to suppress it. Then he says:

But it still comes out from time to time.

(something) comes out

When you're trying to hide something, but it shows accidentally, you can say that it has "come out". For example:

He tries to act like he's all tough, but after you get to know him a little bit, his sweet side starts to come out.

The truth will come out.

Things that often "come out" include:

• secrets
• a person's true personality
• accents
• an opinion that someone has been hiding

(something happens) from time to time

"From time to time" means "sometimes":

From time to time, I'll get a question from a customer about whether they can pay by check.

I make mistakes too from time to time. 

"From time to time" seems like it's less often than "sometimes".