Problem
Monthly membership billing is not billed monthly. The issue is that this membership type needs to be included in the recurring billing rules.
Solution
Follow these steps to include your membership type in the recurring billing rules:
Go to the Accounting tab.
Click on Recurring Billing.
Select Automatic Billing Rules from the menu.
Click on View Rules.
Find the billing rule that should include membership type.
Click Edit.
Click on the Membership Type dropdown.
Check if the Membership type in question is listed. If not, proceed to the next step.
Select the Membership type to add it to the rule.
Click Save.
If these steps do not fix the issue, see Why wasn't the customer's membership billed for a specific month?
By including the appropriate Membership type in the billing rule, they should now draft monthly as expected.