eStatements and invalid email addresses

What are your procedures regarding members signed up to receive electronic statements/disclosures but who now appear to have an invalid email address?  We send an email notifying members when their statements become available on online banking, however, large numbers of these emails are being returned as undeliverable.  Do you continue to send to the bad email address indefinitely or for a certain number of months?  Remove the bad address and stop sending any emails?  Discontinue estatements and start sending hardcopy statements to the mailing address on file?  Just because the email address is not valid doesn't mean that they aren't still accessing their statements via online banking.