I have this same problem since the weekly versions of december (or maybe the end of november) last year.I have a problem with whatsapp and gmail app sometimes too.
They don't sync and advice about new messages until I open the application. How I can resolve this bug? Wipe cache and dalvik?
Background apps like WhatsApp, Telegram and others are not staying in memory. Because of this they can not receive new messages and I will not be notified of new messages.
Only after restarting these apps they will start receiving new messages until they kicked out of memory again.
My "solution" is going back to the last version that worked for me: the stable version 7.0.11.0
Here is the bugreport:
http://en.miui.com/forum.php?mod=redirect&goto=findpost&ptid=192051&pid=4319900