First, it would also help to know which checkerboard we are talking about. Crenicara punctulatum? Dicrossus filamentosus?
C. punctulatum is a fairly hardy fish and tends to be able to handle itself well, for the most part. The fish of the genus Dicrossus are not extremely tolerant of quickly changing water params. They are particularly prone to mortality issues shortly after import, and it's not uncommon to see a lot of deaths when they come in. Scott may very well be correct in that you may be buying fish that are weak and incapable of handling the transition to your tank. They may also be intimidated by other fishes in the tank, adding further stress. Either species is likely to be wild-caught, as neither is commonly bred commercially, so there is a possibility that they carry latent disease or have suffered poor conditions on their way to you. If they are breathing heavily this could suggest gill damage or parasites. Parasites would also provide some explanation about the other deaths, assuming the rummy-nose were not new additions as well.
Basically, looking at your water params, I wouldn't assume they are the cause, but there can be so many more factors involved in making the environment suitable. Also, since the common name involved is not very specific, it's harder to give particulars about what you should be doing for the fishes.
