No, it was on LAN, just wifi, on the router that doesn't have any sleep actions engaged (i.e. it's on always). I'll give it another shot -- I think it was in one of the directories with long list of filenames.
Other than that, I use "Toggle SSH" app for turning sshd on and off. I'll check SBSettings, though.

EDIT:
...
Captain's log, supplemental.
..

It appears the sshd does stop working a few minutes after iPad turns itself off. I didn't really check the timing, but WinSCP reported that the connection was closed.

The log is e.g.:

Waiting for data timed out, asking user what to do.
Asking user:
Host is not communicating for 15 seconds.
Wait for another 15 seconds? ()
Data has arrived, closing query to user.
Network error: Software caused connection abort
(ESshFatal) Network error: Software caused connection abort
Error changing directory to '.....'.

After I chose to reconnect, it would just wait (or eventually time-out); and a second or two after pressing the Home button to turn the iPad on again, the connection would be established again.

(I now use SBSettings toggle, and I've uninstalled "Toggle SSH" app.)

Thanks for sharing :-))

Originally Posted by f4780y

Depending on what device you have and the setup in your home, it could be the wifi signal dropping after 45 seconds of going into sleep mode? Wifi does not stay up and running all the time in sleep mode under certain circumstances and configurations.

So this would actually mean that a few moments after iPad goes to sleep, router eventually closes its connections? (However, there can be notification beeps for new events/news/messages/etc. received during sleep mode, so this doesn't make sense to me.)
(It's on a dd-wrt router, btw.)