As you have pointed out, while your tank may not be cycled, the water changes you are doing is keeping the water safe. So i don't think the issue is your tanks cycle.
You are right, the issue might be from the supplier or from shipping. Water parameters may have got pretty bad during shipping and this is manifesting by deaths over the days following on receipt.
How did you acclimate the fish before adding them into your tank?
What may have happened is ammonia elevates in the bag over time. The water is starved of oxygen, and pH drops. At low pH the ammonia is non-toxic as it will be ammonium. During your acclimating, you open the bag and
O2 rises, pH rises. That ammonium reverts to ammonia and suddenly becomes toxic. Result, fish dying over the following days/weeks. This will all be down to how long fish are in shipping. In these instances, getting the fish out of the water they have been transported in immediately after the bag is opened is beneficial so they arent sat in the ammonia they produced during transport.
Re: Cycling your tank. Are you sure your tank isnt cycled?
Are you seeing ammonia prior to your water changes? If not, you may be cycled. If you arent cycled and the amount of water changes you are doing is essentially keeping ammonia at undetectable levels, your cycle will never establish as the bacteria are being starved of food. While keeping water as clean as possible will be beneficial to the health of your struggling fish, you will at some point need to elevate the ammonia to some degree over a period of time to get your cycle established.