As an apparel decorator, there are many reasons why you may elect to discount a job, but customer pressure is not often one of them nor is simple price matching. If you have properly done your homework on pricing and really evaluated the level of the service you are offering, you will have already priced your product in a way that matches the value you provide. If that's the case and you believe in the value you can provide the customer, you should be firm with your pricing.
In some instances, however, it can make sense to run a job at a discounted rate. If you do offer a discounted rate, you should always make it patently clear that you are running a job at that rate, show the customer the true rate, and explain any justification for the special rate as a qualification that must be met to get the rate again. For example, if a customer must make a certain quota of pieces of the same style and color in an order to qualify for a price break, make that explicit so that when they want to re-order fewer pieces, multiple styles, or try some other variation that isn't profitable, you'll have an answer already embedded in the stated rules from that discounted order.
Another perspective comes from creative hand-letterer and business consultant Sean McCabe, and is one I've used several times. It applies very well to creative services like embroidery digitizing or design that you may have friends and family looking to get at discounted rates. His concept is “full price or free” no matter the relation. In other words, you offer your work either for full price or for free. This helps to cut down on misunderstandings; either the person is supportive of your efforts and wants to pay you for your indubitably valuable work, or you have chosen for your own reasons to offer your work for free.
Other possible reasons for discounted jobs include:
Maintaining a good relationship with a prompt-paying and generally good customer when they are at fault for an improperly approved job. If a customer approves something in sample art that later becomes problematic, but admits to fault and doesn't push for a refund or try to evade payment, we sometimes offer a reduced rate that is profitable, but eschews markups. This allows us to reprint and pay all of our costs and maintain a profit on decoration while making the customer happy and fixing their current job.
When our shop is at fault for an error. When anyone in our shop makes an error, we make it right. Every time, no matter what it costs. Trust comes from accountability, and you can't violate it if you want it to survive and grow through customer recommendations.
When we are courting a new customer that is a good fit for our production. We may elect to waive setup fees or other costs to reduce the barrier to entry for a customer who will provide a solid long-term gain.
To motivate a customer to provide something of value to you. If you want something from the customer or want to incentivize a certain behavior, discounts may be worthwhile. We occasionally will set a discount based on early ordering for holiday company gifts. Since we become bogged down before the holidays, it was worth the small profit dip to even out the production schedule and move some jobs off to a less hectic time for production. Besides, we save money in overtime hours that pays for discounts for the early orders if we keep the schedule even.
Charity. We occasionally decorate for charities, and when we sponsor them, we may elect to reduce or remove costs from the order.
Regardless of how and when you offer discounts, always take the time to explain why your work is worth it. Besides, customers who consistently pressure you on price won't stop at the first discount and they'll push for another discounted rate over time. It's best to make your position known up front and stick to it.