Yes it's possible. Giardia is SO hard to get rid of. You need to bleach all surfaces where she went potty in order to get rid of the infection. When Kirby had Giardia I made sure to clean up after him right away and spray dilute bleach on the aread where he pooped. He was cured after the one course of antibiotics and nobody else in the house got sick. It (and coccidia) can be really hard to get rid of. Coccidia is also hard ot find on a fecal so that may be the issue and not giardia. Do you remember what they sent home as treatment? Coccidia and Giardia are treated with two different medications. Franklin had Coccidia as a puppy and it took 3 fecals to actually find it, I was battling diarrhea for almost a month before he came up with a positive fecal. It may also be the Blue Buffalo causing some upset tummy.
My puppy recently went through this as well.She had tapeworms and giardia so she was put on metronidazole and panacur. She only had soft stools and didn't suffer from full blown diarrhea. Giardia can reoccur (especially pups) and really hard to get rid of. My dogs all do the restroom outside and so it's hard cleaning up back there. Luckily she hasn't caught it again, but it can happen. If your puppy was using pee pads to potty inside then you may have an easier time getting it cleaned up.
I'm super lucky that my other dogs haven't had horrible symptoms though I'm almost sure they have it too. Tomahawk gets soft stools every once in a while but it usually goes back to normal within a day or two. I can't justify constantly having them on antibiotics for something that is really common (at least where I live) and try to deal with it as much as I can before I go to the vet.
My boyfriend now calls me professor poop because I'm constantly checking out their poops haha.
Now you can brag, "I really know my sh!t".
Sanitation is challenging with pets who think turds are tootsie rolls.
Giardia can reoccur. Coccidia reoccurs by nature (medication doesn't actually kill it, just removes its ability to reproduce). Usually what happens is a dog's own immune system eventually can keep it in check. Once it's in an area, chances are your dog's fecal may sometimes come up positive for coccidia, but it's an opportunistic infection that usually only becomes symptomatic in times of stress. That is why so many puppies get it; even reputable breeders frequently have it in their kennels, and the stress of weaning and moving allows it to reproduce rapidly and cause problems. Maddie came up positive one year in her fecal and she was just fine, but we treated anyway. Vet said it's six of one and half a dozen of the other in adult dogs; you may pull a fecal one day and it's negative, next day it's positive, and chances are the dog would never get sick.
I would take in another stool sample. That said, I've heard of dogs who can't handle Blue (it is a good food, but that doesn't mean it works for all dogs). So if all fecals are clean, you might consider the food.
Griffin can't eat Blue Buffalo. It caused bad diarrhea when I first got him as a puppy and again later when he was older.
Unfortunately, yes, reinfection is definitely possible.... I would do another stool check and ask your Vet how often he/she recommends repeating them in your case (maybe monthly for two or three months?), to make sure she stays parasite free and to give her the best chance to recover physically and not stunt her growth. Without this information, you'll be left wondering every time something upsets her and it will be harder for you to sort things out. This too shall pass....hang in there.
I should point out that hookworms are frequently recurring as well, though soft stool is not the most common symptom there.