The cycle is broken if you see ammonia or nitrite. For example, it could happen if the pH drops too low and the nitrifying bacteria shut off. You should get a total ammonia test kit to find out. Also, you can test a sample of pure distilled water as a zero reference. You can test your RO water too, but ammonia can get thru a RO membrane, FYI. If you see ammonia, the short term solution is to dose Seachem Prime, or some other compound that is supposed to treat tap water.
I don't think you need a copper test kit. First, copper won't get through a RO membrane. Second, the liquid test kits are useless because they measure at a too high level. If you want to check for copper, you should get one of those Hanna low range test kits that can measure in the ppb (billion). But I doubt copper is the problem, and Seachem Prime can bind to it anyways.