Are you using the same smtp settings for both sites?
ie if you have this set to true in user.config then it uses smtp settings from the site settings page not from the config file. In that case each site must be configured separately.
<add key="EnableSiteSettingsSmtpSettings" value="true" />
if it is set to false then all sites in the installation should be using the same settings but you need to make sure you have a valid "Default From Email Address" in site settings. A bad address there can make the mail server reject the mail and not send it.
you might also look to see if any errors are being logged related to sending mail under Administration > System Log
See also Email Configuration
Hope that helps,
Joe