Hi Mike, the regular construction line behavior is that they are cleared out at the end of a command, that makes it easier to create as many as you need for a particular point pick without having them stay around and clutter things up.

It is possible though to set up a script on a shortcut key to keep the last created construction line around, there's also a plug-in you can set up which will make a command that you can run to create construction lines and have them stay, the information on that is here:
http://kyticka.webzdarma.cz/3d/moi/#KeepCLine

- Michael