It sounds like they are brackish (between fresh and salt), some brackish fish do fine in freshwater, until they don't. they tend to last ohhh anywhere from a couple days to a few years. You never really know, but most die off withing a few weeks. If you could ID it (google), you could then see if they are brackish or not (the only puffer I know that is truly freshwater is Dwarf Puffers, they stay about the size of a nickel). Also Puffers are mean, it is not a good idea to keep them with other fish they tend to pick them to death. So if they turn out to be brackish you would need to start a new tank (sounds fun), or if they are freshwater, here are some questions:
1. what size of a tank
2. How many fish and what kind
3.what are your water readings
4. Do you do water changes?
5. what have you been feeding them??
If you answer thes question we may be able to help you out a little more. COOL FISH BY THE WAY
Ohhh and do a water change if you have not been doing one, do about 20-25% the first time. Puffers need very clean water. Then about a week later do 30-35%. From then on you can change 35% of the water every week or every 2 weeks (but every week is better)