Make: how to continue after a command fails?

Try the -i flag (or --ignore-errors). The documentation seems to suggest a more robust way to achieve this, by the way:

To ignore errors in a command line, write a - at the beginning of the line’s text (after the initial tab). The - is discarded before the command is passed to the shell for execution.

For example,

clean:
  -rm -f *.o

This causes rm to continue even if it is unable to remove a file.

All examples are with rm, but are applicable to any other command you need to ignore errors from (i.e. mkdir).