Spontaneously deleting e-mails from Galaxy III
POP is primarily a client-based protocol, meaning that the default behavior is for each client (your phone in this case, perhaps Outlook on a PC at home) to download messages from the server. This means that the first client that connects to your account with take all email messages it sees. Then, subsequent checks by other clients won't be able to find anything on the server because all those new messages are now stored only in the first client. POP clients can be configured to "leave a copy of messages on the server," which is highly recommended if you want to use POP on multiple clients/devices.

This sounds like you've got one or more clients connecting to your account that aren't set to "leave a copy of messages on the server," which means they're stealing messages out from under your phone. From your phone, this would look like they're disappearing. The easiest way to test this is to change your email account's password, then only put that updated password in your account on your phone. If the mail stops "deleting" then you can use a process of elimination to identify the culprit client.