Hi,
Poor you and poor puppy! Did you change her food when you first brought her home and how was her poop when you first got her? Sometimes just changing a pup's food can upset their stomach. Did the vet test her for any fecal worms or parasites? I went through 3 rounds of diarrhea with my younger pup at around that age, usually at night. All tests were negative and I hadn't changed her food from what the breeder was feeding her. Maybe it was a change in the water, who knows what it was from? After 3 rounds of antibiotics (2 rounds of metronidazole and a final round of tylosin), things finally calmed down. It would improve on the antibiotics, then go back to diarrhea a few days after the antibiotics ended. My vet also wanted me to change her food on the 3rd round, thinking it might be a food sensitivity. Since she didn't have diarrhea when she came home from the breeder and for the first week or 2, I thought it wasn't from the food. I just kept her on the food she came on. I also gave her some probiotics with the last round of antibiotics. I used FortiFlora but there are other types. The vet didn't recommend them but said they were OK to use when I asked. They also said I could use Imodium but I did not need to. I suspect they see a lot of puppy diarrhea and the approach must be fairly consistent between vets.
If the vet did not check for worms or parasites, I'd ask for that to be done first. They may need to send the sample to an outside lab, not just look at it in their office. A lot of folks mention giardia as a possible cause of diarrhea and it's apparently difficult to detect on fecal tests. I know my pup didn't have it and no other parasites were found, so we don't really know the cause. Your pup may need another round of antibiotics and I'd try not to switch her foods trying to figure out if something else would work better. Several food switches in a short time period can be more problematic than helpful. If you're using hotdogs or other yummy training treats, try to cut back to just saving out part of her kibble to use for training, no other potential culprits like cheese or hotdogs or pupperonis for now. There have been others on here who have gone through this as well and hopefully they'll give you some ideas, too.
I know it's frustrating and hope it's over soon.