It is google implementation of POP3.
I had same problem and switch to IMAP on phone and POP on notebook.

Anyway You should check it on Gmail.com Go to settings and choose Forwarding and POP/IMAP
For POP exist 3 options:
1) Keep in Inbox
2) Archive
3) Delete
You should activate Keep in inbox

Second thing you can try it is select option:
"Enable POP for all mail (even mail that's already been downloaded)"
but in this case be prepare to get a lot of ald mails from google.
Google has bad implementation of option: "Enable POP for mail that arrives from now on". If you activate it you can download POP mails only ones.....
If you want you can fill bug for this on gmail. It is not phone bug