It sounds like you are asking for several things:
1) You want to reopen Terminal windows in the same position on your screen
2) You want the Terminal windows to connect to specified servers
3) You want an uninterrupted connection to the server: so you can pick up where you left off.
I'm at a Windows machine right now, but I believe Terminal.app only does #1. You can achieve #1 and #2 through AppleScript (or appscript) scripts: search and ye shall find. But #3 would require the use of either screen or tmux (or possibly dtach, but I've never used that). screen is more widely available, but I would recommend tmux slightly above screen. They work very similarly, though, so either should more than meet your needs.
You'd run screen (or tmux) on the server that you connect to, and detach from your screen session when you're done for the day. screen would still be running on the server, keeping your shell session alive, and preserving its state for the next time you log in. The next day you'd log in and reattach to the screen session, and be good to go.