The request is unreasonable on the part of the customer. In fact bug fixing often costs much more, and bug fixers usually get paid more than initial builds, because it is often difficult to find and fix sometimes very complex problems.
Your rates are your rates, you have done nothing wrong, you should not lower your rates.
The pleading of poverty on the part of the customer might be true, might not be true, this is simply not your problem.
The only thing I would say though, is a soon as this type of flag is raised in your mind you should start looking for another customer to replace this one.
If you have no other work, you might consider reducing your prices to secure short term work while you search for other work. Or have a frank discussion with him. What is the end goal, what do you need to get there, what is the overall budget left? Perhaps you can change this to a fixed price project and finish it for him. But he is not your friend, however 'nice' your relationship has been, and I would advise against this.
I think of this as money for my childrens clothes and food. How much clothing or food does he want your children to go without exactly? And for what? I bet it is not a charity providing water to drought victims or similarly good cause is it? And with the money he saves, what is he going to do with it? Feed and clothe his own children perhaps? Or make the next installment on his car?