Why does my email disappear from my inbox but aren't deleted?

After like 2 days, my emails disappear from my inbox and I didn't even delete it.

However, (since I use hotmail), when I go on hotmail.com, the email is still there.

Is there a way to keep messages on Mail without losing it in my hotmail.com inbox?

BTW I got a mac and a pc, if it's useful, but I don't use the included mailing system on both.