You cannot archive anything in Manager because every past transaction contributes to your current position. Those billable time entries are referenced by sales invoices, which are referenced by receipts, etc.
But the Billable Time tab itself is a sort of archive. It shows you pertinent information about billable time entries. Yet you virtually never need to go to the tab except to enter more billable time. After that, invoicing is handled from the Customers tab, sales invoice editing from Sales Invoices, receipt of payment from either Sales Invoices or Bank/Cash Transactions, etc.