It's great to have SQL Server Agent Alerts set up to notify the DBAs when something is broken, but if you have emails set to send it's not much use if Database Mail isn't running; and it's not crazy that sometimes it can just stop and not start up.
This should really be part of your automated daily checks. I'm not using policies yet but here's a quick one to indicate if it's stopped and start it again.
Set Nocount On
If Object_Id('tempdb..#Status') Is Not Null
Drop Table #Status
Go
Create Table #Status (
[Status] Nvarchar(100)
)
Insert #Status
Exec msdb.dbo.sysmail_help_status_sp
If Not Exists (
Select Top 1
0
From #Status
Where Status = 'STARTED'
)
Begin
Raiserror ('Database Mail was not running, attempting to restart', 16, 1) With Nowait
Exec msdb.dbo.sysmail_start_sp
End