Now my heart goes out to folks who say to me.. "I spent a lot of money on my logo (or brochure, or web site...), but I don't like it could you design one for me for a lot less than you usually charge?"
I feel really bad.
But I would feel worse spending lots of my time helping them out for pennies.
I don't mind working on a sliding scale and I don't mind throwing a freebie to a charitable cause... but I won't lower my price because someone spent their money with a poor designer.
These might be the same folks that asked for a quote from me and decided that it wasn't in their budget... but now to repair the work, they will be spending more money. It's sad, but if they went with me from the beginning it probably would have been less in the long run!
Your client can buy day old bread for less... but the next day it's moldy and they will have to buy more... or they could buy it fresh ( spend a bit more ) and it will last longer and will get eaten and enjoyed.
Tell your client that spending a little more at the beginning and getting a better product will save them money in the long run.
And one more thing.. if your client changes the scope of the project, you should re-negotiate your fee. I always inform my clients, when I give them a solid quote, that if they change the project brief, there could be an additional fee. I don't always charge them if it's simple, but if they do a 180 degree turn I have no problem getting a bit extra for the work because they weren't surprised. Remember, from my previous posts... no surprises.
Bottom line... you fee should be fair and reasonable... lowering it even more is not fair and reasonable for you.