stty -a in the Terminal, see what your cchars are mapped to. Make sure that susp (suspend) is mapped to Ctrl-Z (^Z) and intr (interrupt) to ^C.
Do you have any programs running that may 'steal' the keypress? Maybe
somecoolapp uses Ctrl-Z to send a zebra Twitpic someplace.
Remember that Ctrl-C will close your window if all the processes under it go away. I don't know how you run your app, but if it replaces bash by using exec, then the 'Ctrl-C closes window' makes a bit more sense. Ctrl-C closes the foreground app, which is the only thing running, which closes the window.
To suspend the process, you could use another terminal window to send the signal. Find the process ID using either Activity Monitor or the
ps command, and in the other window type
kill -STOP <processid>. Unfortunately Activity Monitor doesn't seem to let you send just any signal, and SIGSTOP and SIGCONT are not in the list (at least on Snow Leopard, which is what I can check).