Personal suggestion: use screen on the remote host; it will manage to keep your connection alive for as long as it stays active in a terminal.
Here's what I typically add to /etc/screenrc for quick identification of my screen sessions:
hardstatus alwayslastline
hardstatus string "%{= kG}[ %{G}%H %{g}][ %{=kw}%?%-Lw%?%{r}(%{W}%n*%f%t%?(%u)%?%{r})%{w}%?%+Lw%?%?%= %{g}][%{B}%Y-%m-%d %{W}%c %{g}]"
defscrollback 8192
EDIT : Hints.
The hardstatus string will show a bottom status line such as this one:

The scrollback buffer is also extended to 8192 lines instead of the usual 1000-1500 (depending on the distribution).