How do I stop screen from clobbering my titles?

As documented in the man page, screen looks for a null title-escape-sequence. bash sends this sequence via the PROMPT_COMMAND environment variable (for example, mine defaults to printf "\033k%s@%s:%s\033\\" "${USER}" "${HOSTNAME%%.*}" "${PWD/#$HOME/~}".

To disable this feature for a particular window, I just run unset PROMPT_COMMAND from that window. Of course, one could just add this to their ~/.bashrc or to a specific environment file to make it more persistent.