When several objects are first added there are loads of lovely options to change multiple parameters. e.g curve tree saplings. This is wonderful as you can try out several variations. Then suddenly if hit the wrong button, all these options disappear. So frustrating! How can I get them back and / or prevent the box disappearing? I can't believe that the default isn't for the option box to remain visible until the user actively makes it do so.
Yeah, that's the behavior of that window, it's temporary. It's called the Adjust Last Operation panel, so it'll only show you your last operation. If you make any other operation, it gets replaced or goes away, so you have a limited chance to do what you want to do. It's just the nature of the beast. We made a fun short video about here:
Sadly I cannot get F9 to do anything. I have found that I can retrieve the panel by unchecking the view option under the view tab, and then rechecking it, providing I have not gone to edit mode. This also works if I have clicked on another object, but not moved anything. However if I have changed the viewpoint with the mouse I can retrieve the panel, but only in a sort of greyed out colour that I can only see but not alter. At least then I can make a snapshot of any complex changes I have made to my branching saplings etc. Blender is a great program, but it has some seriously weird foibles. This is a really annoying one.
Omar is correct about the 'Adjust Last Operation' window.
However I think you are using the sapling tree add-on, right?
Same thing applies, once you click on an object, change a setting elsewhere, etc.,
you loose the window.
With the sapling tree add-on you can save your own preset.
At the bottom of the Geometry settings you will see a Preset box to name your preset tree, then click 'Export Preset'
This will save your tree and all current settings, you can then reload your tree from the 'Load Preset' list.
Hope this helps, and limits your frustration with this add-on.