If the Outlook emails fail to be picked up then it is probably some junk SPAM and probably malformed using international character sets. To fix this,
a) In Outlook pick,
Tools -> Send/Receive -> “< the broken account name>” Only -> Download Inbox Headers

b) Outlook will now download just the headers. The first one that comes in (i.e. the oldest one) is probably the bad message that is breaking Outlook e.g. if it is Monday and you are getting emails up until Saturday evening then the next message on Saturday evening is probably the bad message.

c) Right-mouse on that message and select “Open”. It will not have any local message but will ask what you want to do. Pick the last option of,
“Mark to delete this message from the server”

And then do OK.
d) Now do your normal Send/Receive All and all the backlogged messages should download normally and any marked for deletion emails (as above) will be automatically deleted.