Whenever I select lines that I have made with the connector ( ) tool and copy/move/resize ( ) them... they lose their curve. Is there a way to prevent them from losing their curve?

I don't have a lot of experience with the connector tool, but I just played around with it some, to learn the basics.

To me, it looks like the connector lines are not meant to have curves. So that even though you may have used the node tool, perhaps changed the node type and/or created curves, when you copy, move, or resize them, they are sort of "redrawn" and revert to their default behavior.

I looked in Inkscape Preferences, but don't see any options for curved lines with the connector tool. So I think your best option will be to use Object to path, which converts them to paths, and will remain whatever type of path you create when you move, copy or resize. Or just use the pen tool to draw the lines. (Based on my very little experience, I think I would just use the pen and node tools to begin with. Although I think there may be things I haven't yet learned about the connector tool?) However, since it would no longer be a connector line, it won't snap to the object, or retain any other properties that the connector tool features, like Ignore selected object, spacing, etc. Some of these lost properties can be simulated with other Inkscape tools, like Snap to objects, for example. But not all of them.

Well I guess that's my best guess, based on all of 20 minutes using the connector tool. There may well be a better solution, so before you spend a lot of time making changes, please wait and see if anyone else replies with a better idea

Well, it might be possible that there is a better solution for what I'm doing with it. I've been using it as a cheap, fast, and dirty way to make the lines for my drawings that I've done. If there was a better way to ink in general, I would be up for knowing how. I'm a novice when it comes to actually doing digital art.

Oh, if you're just doing regular drawings, not flow charts, I would definitely say use the Pen or Pencil tool, which ever works the best for you. And then edit with the node tool. I find nothing faster or better about the connector tool!

Also see the links in my signature, for some excellent instructional material -- first stop, Help menu!