Mine never was. She did not have consistent training and my parents did not know anything about training dogs. Heidi has occasional accidents her entire life. However, this is not typical. With consistent training and patience, all dogs can be trained. Do you have a dachshund?
Callie is 5, and Gracie is 8, and both are also mill rescues that came to me as adults. They took a bit of working with to get their house-training skills down-packed. It took more consistency, in my opinion, than working with a puppy. Callie and Gracie were doing wonderful, and Callie still is. She holds herself and waits for you to let her out. Same with Rosie, who has never had an accident in the house. Gracie, in the last few weeks, has had a couple small mistakes in the kitchen. She went to the vet and was found with some liver problems, and the vet thinks that's probably the cause. So I can't really blame her house-training skills on it.
Other than that, it took mine a few weeks to get things down-packed and to know that pottying is for outside, and not inside. Really wasn't too difficult, just takes consistency.
My Dachshund Bingo is 13 years old now... he was born blind, with Corneal Dystrophy... and my parents and I did not have one problem with getting him housebroken. We got him when he was 8 weeks old... and he was potty trained by 9 weeks old.
I guess it is just what you do and how you do it.
My sister-in-law and brother in-law have Buddy who's 4 or 5 yrs old now. He's not completely house trained but it's their fault. Those darn puppy pee pads! They also are always making excuses for him such as it's been raining so much, he just won't go outside (enter the pee-pee pads). It's too cold outside for him, he just can't handle that cold weather (enter the pee-pee pads). When we go visit there's always a pee pad by the door (often with a stain on it) and always one in the bathroom. When the bathroom pee pad isn't down in the bathroom, you'd better turn on the light before you go in there because you just may step on a stinky pile.
It's all in the way you treat and train the dog I think. Sometimes people think small dogs are just too delicate to take the weather.
My girl doxie is a horrible breeder rescue. She was raised in a crate that wasn't clean, so she thought the crate was where you went, and then layed in it. Brigit was a pain to potty-train. I'd have to say it took about a year to sink into her head what we wanted. After we started using an ex-pen, she'd let us know she hd to go when she was in there, but never when she was out and about. I counted how many times she peed before betime one evening, and i stopped counting at 15.
MAx, my boy, was ridiculously easy. We got him at age 4(ish), and he'd only been an outdoor dog. He had 2 marking incidents inside, then he had one after his neuter (which I don't blame him for at all), and there's been none since. He was trained within 2 weeks. Every once in a while, he'll get too frisky with my big guy, and if Cerb barks at him, he'll do the fear peeing, but I don't consider that the same as potty training, as he was an abused dog. But, he hasn't done that in a while.