was "I never ever had a problem..." ever useful at solving a problem? you are having a problem now, don't you.
don't you think there would be an outcry all over the internet and also newspapers and tv if outlook.com would start loosing emails? biggest shitstorm ever. this is a problem with your own setup.
what you are experiencing is is most likely related to a standard POP3 behaviour. that is: when fetching email, it gets downloaded to the client but also deleted from the server. i am sure one could change this for Thunderbird. mail-clients on mobile devices might be less configurable. this is why as soon you are leaving the MS ecosystem (by using Thunderbird or an Android phone for example) outlook.com, an email provider that supports POP3 only and not IMAP, is far from being the best option.