There isn’t a specific record retention period requirement for adverse action notices outlined in the FCRA, which is what would apply to DDAs. There is a requirement for 3 years for prescreening and a reasonable period of time for the accuracy and integrity rules. Here is a link to a chart that details record retention timeframes for federal consumer protection laws/regs: chart.
If it has a credit feature attached to the deposit account and there is adverse action taken Reg B/ECOA could apply. The ECOA record retention rule is generally 25 months after notice.