Go to file :
Click Account settings then Account Name and Sync Settings :
Change the Download email for the past:
I have mine set to two weeks, but I set Dan’s to one month.
Then click more settings
Then click advanced tab on the window that pops open.
Untick the box I have highlighted. Click apply
Outlook will prompt you to say it needs to restart to apply the changes. Click ok.\
Then click ok on the next box you are left with. It will prompt you again, click ok. Close outlook if it hasn’t closed on it’s own.
Then Re-open outlook and you should see any updates to the inbox, this is now a completely Live inbox and is only visible when connected to the internet.