Missing map email on iPhone

[serringt]

I've just added an imap email acct to my iPhone 6 (iOS 9.1). The account is large with a lot of unread emails - this is because I've just switched from using Outlook on a PC to Outlook on a Mac and I need to do a lot of housekeeping. The emails are all visible on the Mac and on the web, and the number of unread emails are correct on the phone but a lot of them don't appear on the phone. I've deleted the account from the phone and reinstalled it but the problem persists, although after reinstalling the account different emails are missing.
Might this be to do with the number of emails?

 

[gsmornot]

If you see a badge that is correct, the messages are there. In settings, mail, do you have organize by thread on? If so, you might not see each message right away because it has been sorted in with other messages which can change its placement in the list. (based on the newest message in the thread)

 

[BrianBaughn]

I'll put my money on gsmornot's suggestion. One long shot bet would be some sort of troublesome IMAP folder placement.

 

[serringt]

I've tried switching off "sort by thread" but it doesn't make any difference. I'm pretty certain that the emails haven't been downloaded because if I search by name for a missing email it can't be found. There's a whole time gap - the first time I set up the account it was 5 months, this time it's 2 years