You do not edit resolution - when the field is on screen, it sets the value. You need to change the workflow to clear the field out when you use the "reopen" transition.
Have a look at the (non editable) JIRA Default workflow that ships with JIRA for an example, you'll find a "post function" that says "clear field resolution" or "set resolution to none" on the re-open transitions.
I have multiple projects that use variations of the same base workflow. The variations depend on the requirements of the project or issue type. The variations mostly come in the form of new statuses ...
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