Invoices tend only to stay in draft status when an account continues to be unpaid by the customer.
Need to charge the draft invoice to the customers card?
You are able to charge the invoices when they are in draft status in Stripe. Follow the same steps as outlined here.
Changing the status of draft invoices
If the invoice is in draft status, and you need to change it to paid(as the customer has paid outside of Stripe), void or uncollectible please follow the steps here.