iOS won't let an app keep a socket open very long once it's out of the foreground. (In generally backgrounding on iOS is unreliable. It's a double-edged sword: it keeps rogue or badly written apps from burning down your battery.) People who do a lot of SSHing generally use something like screen on a remote host.

(Actually, using something like Blink and mosh seems like a better idea. See some of the comments below.)