Sending, receiving, and organizing email in Outlook.com
Do you see any “Cannot connect to server” error in Mail?
Remove the account again, then add it back using Exchange instead of Outlook.com. Go to Settings, Mail, Accounts, Add Account, Microsoft Exchange, enter your email, sign in, and ensure Mail is turned on. Then go to Settings, Mail, Accounts, Fetch New Data, enable Push. If it still fails, go to Settings, General, Transfer or Reset iPhone, Reset, then Reset Network Settings. This re-establishes the server connection and restores email sync on your phone.