IMAP mail problems

[viper37]

Can somebody here help me?  My Google research seems determined to tell me my problem is impossible...

I have 2 computers at work sharing the same e-mail account. One is POP3, the other IMAP.
I use Thunderbird.

In the past, if the IMAP computer was reading the mail, I still could get it by refreshing my folders.  Since I reinstalled everything during my vacations, I can no longer get my emails on the POP3 computer if the IMAP account holder has fetched the e-mails first.

I thought it could be because she moved the mails to some offline folders, but they ain't offline folders.

There's no such setting as "Leave mail on server" for IMAP accounts, so I'm lost here as to why it happens, when it shouldn't...

[Caliga]

POP3? Did I get caught in some kind of time warp and it's 1997 again? 

[viper37]

POP3? Did I get caught in some kind of time warp and it's 1997 again? 

I try to avoid Imap when I can.  I like to have my mail locally stored.