Yes a puppy can relapse but this is very rare and I have only heard of one case. Puppies that make a quick recovery, or so it seems, we get alittle overzealous with activity. Keep the puppy as calm as possible and limit the exercise until the vet gives a complete bill of health. They need the time to regain strength and build up their system.
Just a quick note to anyone who thinks their puppy or dog has the virus. There are many occasions where a dog will show all the signs, including the vomiting and bloody diarhhea. What I have noticed is false positives form worm infestations. Alot of vets do not consider that the signs and symptoms are due to the worms. Based on the positive parvo results they will assume it is parvo. Keep in mind, the treatment for this would be the same as it would be for parvo which is subcue fluids and other remedies. Also, a deworming but to be careful not to over de-worm as it can cause death as well.
There are false negatives and false positives. Ensure to ask the vet to check the fecal matter for any worms as well. Very important.