Well....I don't know if I have any "new" ideas to give you, but I sure understand your frustration! I got incredibly lucky with my little girl. I got Keira when she was 11 weeks old, and Dachshunds are suppose to be very hard to house train, and no one believes me when I tell them this, but Keira was fully house trained in only 14 days!
Here is what I did with Keira...... every time when I had let her out of the crate or after she ate or drank I said "let's go potty" in a very happy voice. I took her outside on a leash to the area I wanted her to relieve herself, and let her sniff the area. When she did her potty I immediately said "good girl, good potty" in a very happy voice, gave her a small biscuit treat, and a petting or a rub on the head. I did this each and every time she went potty. After 7 days of this and many, many outside potty trips in the -20 to -30 degree weather (sometimes seemed like every hour or less), I started letting her outside from my patio door on her own leashed to a runner. I stayed right by the door, and watched to make sure she went potty. When I let her back in the house, I continued with the happy praise "good girl, good potty" gave her a small biscuit treat, and petting. I started phasing out the intense praise and treats after about 2 weeks.
She sleeps in her crate at night and is put in it when I am not home. I still say "let's go potty" when she is let out of her crate, and from time to time I will give her a treat when she comes back in the house just to keep her on the right track.
Just remember, puppies have to be watched each and every moment. If you can't watch them they need to be crated or gated in an area that won't be ruined by accidents or so they don't chew on things they shouldn't. If you see your puppy walking around and sniffing the floor, that is your clue it has to go potty and you need to get it outside quickly!
Now when she has to go potty she will go to the patio door and whimper. If I am not in the area, she will hunt me down (per say) and whimper and run in the direction of the door. I say "let's go potty" and make her sit before I put on the tie out runner. I open the patio door and tell her to wait, were she must sit until I tell her "OK".
I hope this helps????
Shelly