Part of every project, no matter its size or complexity or industry, there is some level of effort--hours, dollars, people, tools, etc.--allocated for the pure purpose of managing the project. This includes planning, oversight, schedule and cost tracking and control, managing risks, communications, reporting, metrics analysis, and on and on. This also includes managing changes to the contract. Your dollars that you allocated to the managing the project contain the dollars you need to execute impact analysis of each and every change that hits this particular process. It does not matter if the change is adopted or rejected; you have the dollars necessary as part of the project budget to conduct this analysis.
Of course there is risk here, as there is with every other management task and every other project task. You could estimate too low and overrun your budget but this is what PM is all about--managing your variances, estimating contingencies, deploying those contingencies when necessary, mitigating everything else.
As the seller of services, the assumption is you included the necessary dollars for this impact analysis and your contract type has reimbursed you accordingly. If your sold your project as a firm fixed price, you carry all the risks and hopefully you estimated well to include fat contingencies if you predicted a lot of changes. If cost-type contract, then you need to keep your customer aware of how your costs are accruing in this area and warn them when you are starting to run hot. It is up to them to slow down the requests or fund your overruns, in that case.
If you did not consider changes and doing impact analyses as part of your price, then capture this as a lesson learned and include this in your next proposal. If you have price-to-win pressures, then welcome to the club.
