Hello Mixer
I too use webmail and not a product like outlook ... as I do use different PCs and past experience downloaded all to the PC in use and no later access from another PC. I also use webmail to avoid all data being downloaded to max my limit: I choose what I download! Things may have improved but I won't risk it.
I've just posted in part the following stumbled across fix that might work for you " ... by persisting with settings, I accidentally hit either the date or flag icon/s ... and my emails appeared. I am unsure if it was a combination of both or one that did the trick. ... I had earlier sent a formal complaint today seeking an apology/a stable system/financial redress or an admission of not wanting users. Then after reading other posts re "security settings", I spent 1.5 hours with McAfee re Privacy settings, with resulted in turning that off but to no effect, so McAfee was not the stumbling block as others intimate with their product's settings. ...".
I also use a junky address that I forwarded emails to (pre-Mail) webmail ... and at least I could read them, missing only a few in the cross over period.
Thanks, dw 19/8