What exactly happens in your arXiv account if you no longer have institutional affiliation?
Log into you arXiv account and change your e-mail address.  You don't need access to your old e-mail to do this, nor will you lose your arXiv account if you don't have an academic e-mail address.  (Having an academic address is not a requirement for arXiv participation, after all.)  Once you have an account, there is nothing (short of administrative action) that would cause you to lose ownership of your papers or your existing endorsements.  It should be no different from changing your e-mail in any other account you have online.