It depends on how you shut the engines down. If you just press the engine stop button you will lose a lot of systems, but using the engine shutdown option on the TMS preserves half lighting, doors and so on.
For dwells longer than 15 minutes they really ought to be shut down, but given that most services change crew at New Street it may not be obvious to the inbound driver just how long the train is due to sit. It's also a bit odd to do something like that at the mid-point of a journey and potentially could cause disquiet among the passengers. Voyagers can lose their air relatively quickly but don't generally give trouble restarting.
On meridians, when you key off, you’re promoted to select either station mode (one engine running on a four or five car, two on a seven car) or normal mode (all engines running) on the TMS.
If no selection is made, the train will enter station mode six minutes after keying off, and will fully shut down after one hour. If “normal mode” is selected, engines will run for one hour, then station mode for one hour, then full shutdown. Obviously, if a key is left on, the current mode will continue indefinitely.
The only time the engine stop button would be used would be to abort the engine start process in some kind of emergency.