Hi. When I first brought Buster home he too had Giardia. It also was resistant to medications and it took a couple of rounds to actually get rid of it. Dogs get giardia from water that has been soiled with feces. Buster came from a commercial breeder and I learned that they had been cited for contaminated water. I personally would continue with treatments since Giardia is so easily transmissible and could be compromising your dogs immunity. Good luck I hope the next round of treatment cures the Giardia. I remember how frustrated I was trying to get rid of it with Buster.
Giardia in Dogs - Learn the Signs and Treatment | VCA Animal Hospitals