SMTP connection lost after final dot H=example.com [IP-ADDRESS] P=esmtp
This means the server didn't send the QUIT
SMTP command. It's not a huge problem (the mail has already been delivered by that time), although chances are pretty high that the mail which was just delivered was actually spam, and not a genuine email (genuine email senders don't usually drop the connection like that).
SMTP connection from example.com [IP-ADDRES] lost while reading message data (header)
This means the connection dropped during the transmission of the email itself. Barring any bugs in the sending server, this will be considered a temporary failure, and the sending server will try again after a suitable delay.
In general, you shouldn't need to act upon these messages. If they occur a lot for some sender that you know to be a genuine sender, you might want to verify if there is any connectivity problem between you and the sender.
The more likely case though is that someone's trying to sell you small blue medical pills.