E-Mails disappeared!

WHY DO MY E-MAILS KEEP DISAPPEARING??? I wanted to keep some important e-mails so I could keep track of what was happening. I moved them to a special folder and checked to make sure they were there. Everything was OK for a couple days and then, when I checked, they were all gone!
What happened to them and how can this be prevented?

Hello,

can I ask what email service provider do you use?

regards
Jan