Final answer:
The least likely reason for an auditor to leave a client is if the client uses an accounting basis other than GAAP, as auditors can work with various accounting standards. Other issues like contentious relationships, accounting irregularities, or non-payment of fees are significant concerns that could lead an auditor to resign.
Step-by-step explanation:
The least likely reason for an auditor to leave an existing client among the options provided would be 'c. The client reports on a basis of accounting other than generally accepted accounting principles'. Auditors are familiar with various accounting frameworks, and while a client not using GAAP might present challenges, this in itself is not typically a reason for an auditor to discontinue services. Auditors are trained to work with different accounting standards, such as International Financial Reporting Standards (IFRS) or other comprehensive bases of accounting which could be applicable for certain types of entities or in particular jurisdictions.
In contrast, issues such as a contentious relationship between the auditor and the client, accounting irregularities, or a client's refusal to pay assessed audit fees would pose significant professional and business risks, making them more valid reasons for an auditor to consider resigning from an engagement.