Do we have to abide by the e-sign rules for sending dormant / inactive online banking notices to our customers?

The notice basically tells them that their online banking account will be closed if they don't respond in 40 days.

It's a matter of state law and the terms of your contract. If one or the other requires "written" notices in these situations, then you must use paper or an e-document that your customer approved in the ESIGN-prescribed manner. If your original ESIGN consent was too narrow and didn't cover this type of notice, you'll be forced to do paper notifications (since the customer is not responding to your communications and would not likely respond for the purpose of providing demonstrable consent.)