Kate was spot on the entry to your tank, acclimatization is huge for these little guys they don't like changes much at all temp ph ammonia etc. They will for one just flat out die, and two be very prone it ich if conditions flip on them or are bad in the long run. And by acclimatization not just float the bag, slowly ad your tank water to the bag so by the time they go in your tank they pretty much had a good portion of your tank water in the bag.
But in the end they are not really fragile fish, if they have good conditions they are very hardy and live a good long life. I know people say fish can adapt to non native specs and a stable ph etc is more important then trying to adjust parameters, (that is true messing with ph and kh over the long run is a pain in the butt) but I find you are better off stocking with fish that suit your stable ph. Cardinals really do like and thrive in soft acidic water, they are way hardier and healthier in those levels. My main tanks have 6.4 ph and 2.5 kh with a temp of 80 to 81 degrees and I don't loose cardinals at all. They are nice and fat and bright and not ich prone at all.
I have had tanks in the past that were 7.4 in ph and slightly cooler 76 to 77 and cardinals in those tanks, lived (had some losses, mainly in the first few days) but they were no where near as healthy. They were not nearly as bright, they didn't feed as agressivly, and were way more prone to ich.
The other crucial part of cardinal keeping I would say is plants, they thrive in a well planted tank, they are so much calmer, and the plants keep the water so much healthier and eat up any toxins ammonia nitrite etc very quickly, without them small build ups of toxins takes out Cardinals, either really fast or slowly from disease or damaged tissues (gill etc)
I have dropped cardinals in 6 per batch, into heavily planted tanks with mature filters the day they were set up, with no cycle issues, and no losses. I set up my 50g that way added 3 batches of 6 and in the two months+ since I set it up I still have 18 bright happy healthy Cardinals in that tank, they have pretty much doubled in size in that time and are very bright.
Basically plants, water parameters (good,stable ph and kh) and stable temp on the high end, if you have those, you will have no problems with these fish. You will have nice fat 2 inch beauties in no time, they grow quite fast when well feed and are healthy.
They also shoal nicely with neons for the most part (they split into groups but do mix a fair chunk) , here are young cards and neons of mine peacefully wandering around the tank.
