Will an organization retract a grievance at a complainant's request if said plaintiff claims to have filed it during an episode of mental or physical illness, or are the records kept regardless of the circumstances/outcome?
This is a practically-unanswerable question. The answer depends on the particular institution and its policies, and the discretion available to those in charge of hearing a grievance. So this is the general outline of the legal considerations. A professor has a property interest in his/her job and related privileges, and grievance procedures threaten that interest. In some cases by law and in all cases because of the interests of the university (to not get sued), the university has an interest in only pursuing complaints with merit. If, and only if, there is reason to suspect that a professor has violated a university policy, the university grievance procedures will mandate pursuing an investigation (which could lead to sanctions).
If there is additional reason to suspect, beyond an individual complain, then the procedures probably mandate that the investigation continue to its conclusion. The specific procedure at my former institution was that every administrator (chair, dean, provost) has the power to terminate an investigation, and those recommendations are influenced by various committees (e.g. the Faculty Hearing Committee, which evaluates the evidence presented to it). The committee has ad hoc discretion to dismiss, or to recommend sanctions (there were no concrete guidance documents / rules).
There is no general rule that an institution must cancel a grievance procedure in response to a petition by the allegedly aggrieved person. There is a bit of reason to hold that they should not do so, because ignoring complaints pertaining to protected class status can be very serious. So if there is a complaint alleging sexual discrimination, the university must respond appropriately lest a "pattern" of discrimination develop, which has very negative financial consequences.
As you describe it, you did not actually initiate a formal grievance process, so you cannot retract one. You can deny / retract a prior allegation, which may or may not affect an official procedure if one had been initiated.