not sure if this is your scenario, but I have observed that if you start either the admin server or a managed server via putty in the background (including if you use nohup), the started process will usually die if we close putty by simply closing the window (i.e. clicking the "x" of the putty window). If you make sure you exit completely from your shell in putty (ctrl-d until the shell no longer responds) and then close the window, the process remains running as expected (for me this is observed behavior for starting WL processes via Putty on RHEL3, RHEL4, and RHEL5.
If you are not doing so, it is good practice to use "nohup" if you are starting a background task on Linux from putty. nohup disconnects the calling terminal from the application so there are not ties of stdout/stderr to the shell created by your putty session.