I'm really sorry for your losses :(
It sounds like you are having a problem that has been dubbed new tank syndrome. . .
Basically, you start out with clean water - but the waste from the fish and their food turns into toxic ammonia. After some time a bacteria will grow in your tank that can convert the ammonia into nitrIte, which is only *slightly* less toxic to fish. When the nitrIte has been present in your tank long enough, yet another bacteria will develop which will turn your nitrItes into nitrAte. Nitrate, as long as it isn't in a very high concentration in your tank, does not cause the fish harm, and is kept in check with weekly water changes. In a fully cycled tank, it is very rare to see a level of 0 nitrates - unless it is very well planted and lightly stocked.
It's possible that you didn't have this problem before because the fish were in a larger tank, and so the effects of the cycling were perhaps diluted enough for the fish to survive it with you being none the wiser.
You can use media from the filter on your old tank, as well as gravel or tank decorations to help your QT tank cycle more quickly, as these bacteria are already established on the surfaces of your older tank. . .
I hope this helps you out. . . Here is a link that can explain things a bit more clearly for you, I hope; A Beginner's Guide to the Freshwater Aquarium Cycle
Again, I'm really sorry! Bringing fish home from the shop only to have them die is very distressing. . .