Sorry to hear about the loss
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It sounds to me that you may have an environmental/water issue. I recommend that you go to a knowledgeable and reputable LFS (local fish store) for information and guidance to find out what's going on. If they try to sell you anything but a book and test kits...walk away!!!
Test kits to buy...if you feel inclined to go deeper in this hobby:
pH, kH, NH3, NO2, NO3 and GH
Aquarium Pharmaceuticals make a good bang for the $$$ test kits. Otherwise a good LFS will test the water for you for a nominal fee.
The next part is interpreting the tests. Post the results for the aquarium and tap/source water and go from there.
"...the guy at Walmart told me that fish tanks are a self sustaining bio-system"
Unfortunately, he's way off the mark on that point in your case. One cannot create a self sustaining system in a 20gal. Guppies yes, goldfish definitely not.
In a nutshell, filters are primarily a place for bacteria to convert fish waste (ammonia), which is toxic to a relatively non-toxic form (nitrate). Without doing partial water changes w/a gravel vacuuming device of 25%, nitrate will build up and any new fish added will not be happy. The present fish will be used to it as the levels have increased slowly.
Just adding water to compensate for evaporation w/o physically removing water is another area of problems down the road. Only water molecules leave the aquarium and the "salt"/dissolved minerals stays behind. When you add tap water, it also adds minerals that's already present, so longterm with this practice you will have a high mineral build up. Technically you should be using distilled (316 stainless steel/titanium condenser) or reverse osmosis (RO) water to top up.
There are quite a few other things to look into as well but I think you have enough info to digest
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HTH