The old Chattermail on PalmOS had it.
Profimail on Symbian has it.

Email for webOS needs a setting for "work hours" where you can tell it to detach from IMAP IDLE and stop checking POP email outside of your work schedule.

For instance you can tell it to only check email from 7 AM to 7 PM, Monday-Friday.

Right now you have to turn this off manually which is quite the pain if you have more than one email account.