How long after payment of an invoice can you examine the billing records of a law firm?

I do not think that payment of an invoice forecloses a law department from challenging any charges on it at a later date. Prompt payment arrangements expressly reserve such a right, but otherwise what is the law for how long the law department has?

One law department’s outside counsel guidelines reserve the right to reopen a bill for up to one year following receipt of it. The department also preserves its right to "examine the billing and disbursement records of the firm" which creates a right to a deeper inquiry than simply a review of an invoice.