If for some reason (material shortage, schedule, etc) I can't provide what the customer wants (or thinks they want) I have a reply that has worked very well , kept them from walking out the door and gotten future work..... here's basically what I say:
"I'm so sorry I can't provide that specific product right now but perhaps some drop off material would work for you?" Then offer what you CAN do for them. It shows you want to help them, that you have compassion for their situation and are willing to work with them. I rarely have anyone walk away and if they do, they don't forget how they were treated for the next time.
Stop stressing about it.... we can't do everything for every situation but we can always make the customer feel valued and that in turn helps the way we feel about these high stress, annoying situations.
You say it's costing you money but why? You either make a sale at that moment or not. If you're taking on too many things (and we all do this) that is causing a production problem then you need to evaluate that and adjust. I'm not putting you down, just speaking from experience.
Inventory is important but you don't have to have so much of it that you end up sitting on a bunch "waiting" to sell it. Have a wholesale
sign shop like
Signs 365 or a local company that can help take the pressure off. Are you friends with the other
sign companies in your area? Many of the shops that are my "competition" have been extremely helpful in situations like this and we help each other often.
Hope some of that helps, good luck!