In what appears to be an escalating incursion into a user’s digital privacy, a collective of film companies continue to implore the court to compel Reddit to surrender its users’ personal details. This move is part of an ongoing piracy liability case against Internet Service Providers. Reddit, however, steadfastly resists, staunchly defending its users’ rights to anonymous speech.
You can use the email for password reset, so it must be stored by the instance. Whether or not it gets overwritten is up to the instance, so it's good security practice to assume it's stored in perpetuity unless you have reason to suspect otherwise.
On my instance it stays in backups for up to 7 days. But if I ever get a request for providing email address because of pirating, well it's a known fact backups do fail sometimes.