Customers can be unreasonably impatient but catering to their impatience can win return business. On the other hand, not catering to their impatience can lose return business. And the key to meeting impatience (within reason, of course), is effective production planning.
The fact that an order held up waiting for artwork, one or more essential supplies, or a production bottleneck, is an inefficient way to run a shop, the cause of a delay is of no interest to a customer; they just want their stuff on time.
It’s true that customers are often unreasonable in their delivery demands, but that’s just a reflection of the type of society we live in nowadays. Remember the one-hour photo printing services? There was hardly ever a good reason for wanting photos printed in an hour when all one was going to do was look through them and then put them in a drawer where they would be forgotten. But that’s the kind of unreasonable impatience a lot of customers have.
So, as annoying as it can be, you have no choice but to deliver when (if not sooner) than expected. This is why orders have to be planned to ensure that there are no production and delivery delays. There must be no waiting for any of the elements of production: artwork, screens, shirts, ink, staff, etc.
On or before-time delivery can go a long way to persuading even the most impatient of customers to bring you repeat business.