Auto-replies have to be set up on the mail server. Mobile apps are normally not connected to the server 100% of the time which is required for auto-reply to work as intended.

The exception to this are Exchange accounts where Aqua Mail supports the feature as it is possible to communicate to the server when an auto-reply is needed in real time. The setting may be found by long-pressing your account and then "Out of office". Alternatively, it can be accessed via Settings > Manage accounts > Your account > Out of office.