The normal usage of the resolution field is "blank until we resolve or close the issue". The standard workflow reflects this - the resolution is not offered to the user until they hit a transition goes into resolved/closed.
If your problematic issues are all open, that would explain it. If you do have resolved or closed issues (and I do mean actual STATUS here, not RESOLUTION), then check that when your users resolve/close an issue, the field "resolution" is offered to them. If it's not, you may need to check the "screen" being used in the workflow, or that the "field configuration" does not hide the resolution field.
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