M.O.
I could've been your daughter, 30+ years ago.
I don't think I owned a mitten for longer than half a day, ever, as a kid. And if I actually managed to bring the homework I had completed IN to class, then that was a very good day.
I'm STILL hopeless about losing things. The only difference is that now, now that I'm all grown up and need kindness less, people are kinder to me about it.
What I'm trying to say is, your daughter is losing things because she has a propensity for losing things. Much in the same way that dyslexics have a propensity to have trouble reading, and people who are tone-deaf have a propensity to sing off key. It is NOT HER FAULT.
What you can do, rather than punishing her, is help her. Sit her down, say, "This looks like a challenge for you. And that's okay. Everyone has challenges. For example, I have a hard time with _____. But since this is a challenge, we have to come up with a solution. So let's start working on a plan." No shame. No blame. But don't completely let her off the hook. Instead, work WITH her on a solution.
A few tips I'd recommend are:
1. Empty out her backpack and come up with a system. Mittens live in this little pocket here. This is their cute little cozy home. (Honestly, if she can anthropomorphize something, she may take better care of it. That still works for me, to this day.)
2. Get her into the habit of an "essentials check." Before she goes through the door, she should give go through a checklist. "Snow pants? Here. Fleece? Here. Gym shoes? Here."
3. If you really want her to bring something home, stick a note where she'll see it, say, on a school binder: "I love you, honey. Remember to bring X home!"
4. Build in some redundancy. I have several sets of backup keys, just in case. Saves my life.
5. She just may not be at a stage where she can have very nice things. If you're getting something that needs to come home in a backpack (as opposed to something that gets worn all day) then buy it used, or as cheaply as possible. Not as a punishment, just to save you both the grief.
And, please. Be kind. Reread Jane Eyre. The charter Helen Burns, an absolutely saintly little girl who was treated terribly for being a space-case and a slob. That's your daughter right there.