Hi...
I've had exactly the same issue with my iPhone 4 but only on 1 of my 2 Hotmail accounts, and totally out of nowhere. I'd not changed any settings, passwords or authentication - it just decided to stop sending emails but still allowing me to recieve them.
I did the following and it worked straight away - clearing my outbox...
Settings > Mail > select affected email account > Outgoing Mail Server > Primary Server > (I selected smpt.live.com > enter email account password (this was showing 'Optional' in this box) > Return/Done > password was checked/authenticated and emails started sending.
I would just make sure you delete any emails in your outbox that you don't want sending before you do this.
Hope this sorts it for you & good luck!