Are there any regulations requiring a bank to mail a monthy DDA statement to a customer that does not have any activity for that month?

No, in fact the only requirement a statement be sent if there is EFT activity. If the account has had not EFT activity in a month, no statement is necessary. But you must send a statement every 90 days on the account, even if no activity occured.

I believe there is an exception for inactive accounts and the financial institution can define "inactive" (such as 90 days). Reg E 205.9(b)3 states, "Inactive accounts. A financial institution need not send statements to consumers whose accounts are inactive as defined by the institution."