I am among the many people having this same problem. I will be composing a new email, whether by clicking "New" or by replying to a message I just read, and Microsoft randomly interrupts my typing and archives the most recently viewed email in my inbox.
This is likelier to happen if the user actually navigates using the tab metaphor Microsoft has introduced. By this, notice I mean that when you create a new message, at the bottom of the screen, the message is being typed in a new "tab." The previously existing tab is usually Inbox.
If you tap on that Inbox (or equivalent) tab and then navigate to another folder/email (to check details of another email, whatever), after which you tap the new email composition tab again to resume typing your email, almost always (in my experience), Hotmail--cough, sorry, Outlook--will interrupt your typing and proudly let you know it's archived a message.
Of course, then you click undo and try again just to type your message in peace, or worse, navigate to see what was archived (from the Inbox tab), unarchive that email, and return to composition, when Microsoft will--again--physically interrupt your typing and randomly archive an email once more.
I've found a bit of a workaround, which is to highlight, say, the most recent word you were typing in the new email, tap Delete (Backspace on some keyboards), and then continue typing your message. Almost all the time after that, Microsoft will stop interfering with that email's composition by randomly archiving another email.
This issue is characteristic of Microsoft's slipshod composition of the email client generally. Load times, while Outlook proudly displays you an email animation, and browser resource consumption (how many see the message that the tab is using too much energy?), are excessive. It's as if Microsoft is determined to ignore good web app standards and push a traditional fat client (meaning, installed software) into your browser, one laden with unnecessary complexity for the simple, everyday task you are trying to perform.
How many of us sit and watch the email animation for 5+ seconds before we can just see our inbox? Microsoft thinks you want to see their animations instead of simply getting on with why you opened your email.
The problem here, in general, is Microsoft's determination to recreate the (installed version of) Outlook software experience in a web browser. Maybe a bunch of old people are responsible for this product, and yearn for the heyday when Outlook was basically an email monopoly. Comparing the Outlook experience--load times, ease of use, energy efficiency (which matters, because it determines how many tabs you can have open in your browser stably)--to other email apps, such as Gmail, leaves Outlook obviously wanting and inferior. BTW, Gmail is merely an adequate client. It's no paragon--but it's a significantly better user experience than Outlook, so much more responsive and easier to use.
The problem with Microsoft is that Microsoft believes a product is always better if it features more useless complexity, and graphics/animation, if it hogs resources, etc. Microsoft became dominant by having a symbiotic upgrade cycle with PCs. The software kept requiring faster processors, more disk space, more memory, etc. So users needed to upgrade computers. Manufacturers responded, of course, by helping Microsoft capture 98% of the desktop market (installing its OS and apps as defaults).
Microsoft has never moved on and un-learned that lesson in a browser-based world. So it keeps making your experience slower, more complex, lower performing. That leads to mistakes like physically interrupting you in the middle of merely typing an email, randomly archiving another email, and trumpeting this unwanted action as an accomplishment instead of what it is: a poorly planned annoyance and disruption.
Even Microsoft's support response effectively blames you: Microsoft tells you your backspace key is now a shortcut to archive. Really? Was that wise? Was that helpful? Anybody with a clue knows that a keyboard shortcut should be a combination of simultaneously pressed keys to avoid bad user experiences exactly like this and ensure the keyboard shortcut is what the user meant to do. That is, anybody but Microsoft, who think the problem is you dared to use your backspace key when they've decided it needs to invoke a feature you may not even like to use at all.
In short, Microsoft thinks the world needs to change to accommodate Microsoft. Unfortunately, as I said, that's a lesson never un-learned from when Microsoft had an effective monopoly. Any sensible software company would update its email client to correct this unfortunate outcome. Don't hold your breath waiting for Microsoft to fix this.
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