In order to solve the issue that Accounting period remains closed after reopen period button is clicked, ensure that the Inactive checkbox is not marked.
Setup > Accounting > Manage Accounting Periods
check Show Inactive box.
Unmark Inactive box for the period need to be reopened > Click Submit
Navigate to Setup > Accounting > Manage Accounting Periods
Click Checklist icon for the period intended to be reopened
Click Go To Task button for Close Task
Enter Justification
Click Reopen Period