No. A bank levy is a ONE-time levy that can be issued many times. The IRS recovers the sum of the account on the day it hits your bank, limited only to the amount owed to the IRS. The bank must hold the funds for 21 days before they remit the funds to the IRS. This does not freeze the account, as many banks falsely advise their customers. It only captures the amount in the account on that day, up to the amount of what you owe. So, it is possible to still do business in the account after the levy.
As you might guess, the 21 day safe-harbor is an excellent time to explore a collection alternative with the IRS in order to prevent a future bank levy.