Please verify if you are using latest firmware datecode 20121208, Firmware Revision: 2201057_231926
There is an fix available while sending email through intranet in this firmware roll.
Use the following HP web link to download the readme file & firmware:
If the SMTP server settings & alert settings are common for both the printers, then may be the email server is not allowing the device to send emails unless allowed to do so. May be you can have this checked with the web server administrator.