Outlook Mobile App Doesn't Refresh Inbox

Outlook version
Outlook 2013 64 bit
Email Account
IMAP
I have been trying to figure out why my mobile email never seems to sync my inbox automatically. I use an iPhone, and have tried several different mail clients including Outlook and Apples mail app. My email account is with AOL, and the best thing I found to work was using AOLs mail app...generally the badge icon displayed the accurate number of new emails. I use the Outlook app on my desktop PC and it works great, I thought for a while that leaving it open may intercept new emails preventing them from being delivered to my mobile app but it does not help if I I close my desktop Outlook app.

As a side question, I am also curious how to get my mobile app to use the same spam filtering my desktop app uses or has learned over the years. When I open my mobile app it then syncs and displays tons of spam which stays there until I open my desktop app which uses its spam filter and moves them to the spam folder. I thought leaving my desktop app open would act as a mail server and automatically move spam with the mobile app reflecting how my desktop has moved the spam. If I mark them as spam in my mobile app it does not route them to the same spam folder in my desktop app.
At one point I even ran 3 or 4 mobile email apps at the same time to see which would sync and receive new emails first or most consistently but that seemed to work even worse, as if it had too many options so it just decided not to send them to any of the apps at all. So I tested them independently and you could wait for days for the badge icon to show the number of new emails, the apps only sync when you open them...I looked hard in the settings for a sync or refresh-rate setting but there is none. I really do not want to rely on AOLs mobile app because I have other email accounts I want to add to my phone. I made sure my desktop and mobile app(s) were configured as IMAP, because POP will be a mess if I am using both mobile and desktop mail clients...plus I would rather have the security of my emails being on a server somewhere.

Any ideas? Thank you!
 
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