Outlook (this if from experience) simply does not handle large anything folders well, especially imap - hence the click at the bottom of a folder to see more (ie history) ??
I don't think this is limited to imap, also in an exchange environment you have this 'click'. It is super annoying. I have been asking (more like complaining) a lot about such issues. And the ms morons are only giving me conflicting workarounds.
I have been losing emails also in this setup, and the way to solve that, was creating a new profile. But at that time I already lost countless of mails. Found even an old thread about this on outlook, just never fixed by them. The development of outlook is flawed in so many ways. I asked them if they do not consider developing this product seriously, maybe they should make it open-source so others can fix things. Shortly after that my account at ms was cancelled (without any notification / warning or whatsoever)
I had a customer spending 700+ / mth to telus because people were leaving emails behind (out of sight out of mind)
I am currently running the exchange setup disconnected from the internet. If you leave it wide open, you get what happened at Rackspace.
that being said the best you can do with outlook is set to auto update the send/receive settings to every 5 minutes or so
A 3G email box is an issue no matter what as the size is the direct issue of the lockups, and/or the quantity of emails in the folder
Outlook seems to work ok until about 200 emails (max 1000) in a folder and maybe 1G of actual data.
What needs to be kept in mind is that Microsoft (espically 365) is trying to push exchange protcol and has all but dropped support for IMAP.
Indeed everyone needs to be pushed to their cloud, that is always what needs to be at the back of your mind when you decide to use this. Although I can't believe that the exchange environment in their cloud is anywhere near similar to the exchange on premises. The latter is such a buggy setup, I stopped offering it to clients.