What year should audit fees be recognized in?

The year under review. Accrue it as with other expenses.

Audit fees should be accrued in the period in which the work is performed.

While I have always accounted for the audit fees this way (accrue in current period) although the actual work is done in the following period, our auditors, Grant Thornton, told me a few years back that it could be done either way: either in the year that is under audit, or in the following year when the services were rendered. Obviously, once you adopt a policy, you need to stick with it.

Actually it could be both in the year it is being audited as well as in the subsequent year. If interim field work occurred prior to the end of the year being reviewed, then that is an expense for that year. The actual fieldwork subsequent to the year being audited becomes an expense for the year in which the service is provided.

We went back and forth with our auditors regarding this point. They sent over this from the AICPA:
AICPA Technical Practice Aid 5290:
.05Accrual of Audit Fee
Inquiry—A CPA has been engaged to audit the financial statements of a client company. The audit is being conducted after year end. Is it proper to accrue the audit fee as an expense of the year under audit?
Reply—According to FASB Concepts Statement No. 6, Elements of Financial Statements, paragraph 145, “The goal of accrual accounting is to account in the periods in which they occur for the effects on an entity of transactions and other events and circumstances, to the extent that those financial effects are recognizable and measurable.” The audit fee expense was incurred in the period subsequent to year end. Therefore, it is properly recorded as an expense in the subsequent period. However, fees incurred in connection with planning the audit, together with preliminary procedures (for example, confirmation work) would be accruable for the year under audit.
In our case, we didn't have to re-class due to a lack of materiality.

The audit fee is an expense in the period when the services are provided. There is long-standing guidance on this issue in the AICPA Technical Practice Aids (reference is TIS Section 5290.05). Accruing the whole fee in the year subject to audit (i.e., prior to all of the final fieldwork and reporting) is not GAAP.

Just ask the CPA firm to provide you with their WIP to date as of the end of the period so you know what to accrue. They always know what their un-billed revenue is at any point in time, in the case you don't have a fixed fee.

Recognize the cost associated with the work performed. In your agreement with the auditors, mirror the billing schedule with the hours performed so you don't need to over-think this.