1) Whether it consitutes a resignation "depends"--that is, it depends on the specific wording of your letter (e.g. if you wrote, "I will be unable to work without a reduction in hours," that could easily be legitimately taken as a contingent resignation; i.e. that will resign if you don't get the reduction).2) Whether the employer would need to accomodate a request for reduced hours due to job-related physical impairments also depends--first, do those impairments rise to the level of a "disability" under the law, and second, *can* the employer reasonably accomodate you, which means, is there some job you reasonably could do there for reduced hours (they don't need to invent a job they don't have a legitimate need for to make it possible  for you to work reduced hours).3) Note that if you don't have an employment contract, you are an employee at will, who may be fired for pretty much any reason other than illegal discrimination (such as discriminating against the disabled; see (2) above)).Given that the specific facts--the wording of your letter, your physical condition, whether you could be accomodated--will determine whether your were improperly terminated or not, you need to discuss this matter in detail and confidence with an employment attorney.