Work constructively with good customers

I am mostly in agreement with dan1111, that in many industries or situations it pays to be flexible with the customer within reason. Demanding payment for every small thing creates friction, and can make the customer scared to call you for some items which could have lead onto bigger projects; when you have a smaller pool of customers, you need that contact time to be able to discuss future projects.

Having said that, unlimited pieces of work are not ok.

Take a new look at how projects run, and expect to do some finishing up work

The solution I've seen used in small software businesses is to expect to do some additional bits and pieces. So a project looks more like this:

| Prep/Tender  |  Specification  |  Work  |  Integration | Loose ends |

If you are currently charging only for the Work portion, you will rapidly drown. It is not the vast majority of the work, nor is it often even the largest chunk. But for the project to succeed (delivering value to the customer and paying you adequately for the whole exercise) you need to be charging an amount that covers the whole lifecycle.

Be a company, not a resource

So I think the problem is one of approach; don't think of chargeable work as the Work segment, and often it is best to avoid a charge-per-hour basis because it suggests to the customer that your time is available to be used in that fashion, like a long distance call or a temping agency. In fact, you want to be able to schedule work in for the next few months/year and last minute changes are not just 'normal' charges. I think you also need to include some amount of additional work into your time budget for the project. If you always see small changes as a problem (whether you charge for them or not), then you will resent these items. But in fact your customer may highly value your ability to work with them constructively.

There is a lot of balancing to be done here, and that is why this work is usually done in companies rather than as an individual; this whole thing takes management and ideally the fluidity of multiple employees to take on spikes in work. So you're having to do this by yourself, but that doesn't mean it can be ignored.

Flag up low quality customers early

As others have said, the kind of customer who wants a rock-bottom price and then tries to squeeze in a lot of last minute extras is not the customer you want. With the above approach, you at least get to find that out when you talk numbers and include the other parts of the project. Ultimately, this is not deception, it is reality; a well-managed and resourced project is far better for both parties, and the more the work can be done up-front the better you will both feel. Bad customers should be evident early if they question this.

Draw the line, quantitatively

Your time is valuable, so I don't think this is an endless pot. If you have set aside say 0.3x the 'work' period for loose ends, then once you reach a threshold (0.35x?) you need to inform the customer that you will be billing. But since you explained up front that you were including some time for necessary loose ends at the end, they will not get this bill out of the blue, which could happen otherwise. By drawing a line this way, you won't have to fret over a single additional item and whether to include it; you can't often tell when you've got to the last item, and can find yourself avoiding confrontation by just accepting a drip-feed of tasks unless the line is drawn before you start.

Master the art of project management, particularly specifying

Finally, be as clear as possible at the Specification stage what you are promising to deliver as part of the job, and what you are not promising. Use previous projects and requests for additional work to inform that specification and ask questions about things that often come up. By the Pareto principle it will most often be the same things that come up, so you really shouldn't be surprised by that. The clearer you can be about responsibilities at the Specification stage, the better you can handle this latter stage work; if it is something you specifically excluded, charge for it. If it is something you took responsibility for, suck it up. If it's neither, add it to your list of things to ask next time.

TLDR It is possible and often preferable to be flexible with customers and do extra tasks that need doing for the success of a project without it being a loss for you, by taking a wider view of what is part of the project and being clear about what you will consider additional work to be charged for.