Thank you for getting back to me. The biggest problem is that your tank isn't big enough for two goldfish. I'll explain. Goldfish produce a tremendous amount of waste for their size. It used to be recommended to have one gallon (about 4 liters) of water per inch of fish. that still holds true for tropical fish, but not for goldfish. There are various recommendations, ranging from 2 gallons (8 liters) per inch of fish to 30 gallons (about 113 liters) per fish, regardless of size. So, even going with the minimum recommendation, Goldberg is ready to be moved into a larger tank. As he grows, he'll need more and more room, and if you want to keep more than one fish, you'll need an even bigger one. I’ll share my own experience with 18 inches total of goldfish (3 fish). They are in a 90 gallon tank. I have an undergravel filter, a hanging filter, and a powerful canister filter. It takes all three of those filters to maintain perfect water quality. Regardless of tank size, frequent water testing is needed.
What probably happens is that w hen you introduce new fish, ammonia and nitrites build up in the water. When that happens, the weaker fish will die first. New fish from the pet store are often not in the best of health, so it makes sense that poor water quality would affect them before Goldberg. After the new fish dies, your water changes and cleaning improve the water, keeping Goldberg healthy. Chances are the first fish you got lived longer because Goldberg was smaller then, and it took longer for the water to become toxic.
I suspect the water quality is never good, but isn't bad enough to make Goldberg ill. At 3 years of age, he should be bigger than 3 inches long. Mine usually reach 3 inches by the time they are one year old. When conditions aren't perfect, growth is slower. That being said, you have done much better than most people do with goldfish. Few goldfish live to be more than a few months old because they are kept in bowls, not tanks. But, the time has probably come to upgrade to a larger tank for Goldberg. Goldfish are somewhat social, but they also do well alone. If you want to keep only Goldberg, I would get at least a 10 gallon tank (and expect him to outgrow that in a couple of years). If you want to add a second fish, go with 20 gallons.
When setting up a new tank, there is a process called cycling which you need to be aware of. The nitrogen cycle, in which ammonia from fish wastes is changed to nitrites and then nitrates has not become established. That results in changing levels of ammonia and nitrites and puts a lot of stress on the fish. It also reduces the amount of oxygen the water can hold, and the fish will often gasp at the surface. cycling is very hard on fish. Some pet stores recommend making the fish suffer through the process, but often, they will die. There are other ways to cycle a tank. The following website gives detailed instructions and also explains cycling in depth. It will help you understand what happens.http://animal-world.com/encyclo/fresh/information/CycleAquarium.php
Once the tank is cycled, we never want to change all of the water. That destroys the good bacteria, and the whole process has to begin again. Weekly water changes of 10%, along with vacuuming the gravel with a siphon, are the best cleaning measures.
The best thing to do would be to get your new tank and cycle it according to instructions on the link I gave you. Leave Goldberg in his present tank until cycling is complete. Then, if you want another fish, move Goldberg to the new tank, but leave the old tank set up. Any time you bring a new fish in, you risk introducing a disease. It's best to quarantine new fish for 30 days. If the new fish is healthy after that, it can be put in with Goldberg.
If you have more questions, let me know in a REPLY. I hope that whatever you decide to do it will work out well for Goldberg and other fish you get.
My goal is to provide you with excellent service – if you feel you have gotten anything less, please reply back, I am happy to address follow-up questions. Please remember to rate my service only after you have all the information you need. Thank you!