May be there is condition involved in the workflow, or user in role does not have certain permissions.
Can you please include screenshots of workflow options page and permission scheme of related project.
Or follow these steps,
Check whether user in role has transitions issues permission, if its involved with setting fix versions field the user should also have resolve issue permission.
Now coming to workflow, go to the transition where user in role cannot change the status in edit workflow page, check whether any conditions are configured.
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