Remote system no longer responding

Hello.I have other problem

I have two servers

If I use the address for Lotus Notes server1 to server2 no problem

but

if I use the address for internet then I have next error:

Router: Failed to connect to SMTP host server1.COM because : Remote system no longer responding

I can send emails from server1 to server2 with the direction of Lotus

but if I use the Internet address can not send emails

name1@server1.com that is not working for name2@server2.com

and also name2@server2.com for name1@server1.com can not deliver mail

but the servers are receiving emails with the address lotus

and also receives and sends mails to a hotmail.com, yahoo.com, ibm.com. and more.

I have the same public IP for both servers

I have different private IP

Do you help me please

Thank you very much