Mail can only be routed to you if you're available in the Email, Task, Voicemail Channel.
How Mail items are routed
When you initially go available in the Email, Task, Voicemail Channel, and if there is a Mail Conversation waiting in the queue, it will automatically be routed to you. You must click Next or Close & Next to receive additional Mail Conversations.
If there are no Mail Contacts waiting in the queue at the time you go available, the following item that comes will automatically be routed to you, then you must click Next or Close & Next to receive additional Mail Conversations.