I guess it's possible that switching off your wireless adapter is actually causing the issue. I don't actually know how SkyDemon determines unique computers though...

You could try this... Instead of switching WiFi off, why not just set your LAN to have priority. It'll save you hassle as well...

I'm assuming Win7 here...

Go to 'View Network Connections', then hold ALT and click on Advanced > Advanced Settings. On the 'Adapters and Bindings' tab, you can reorder your connections. Windows will use the topmost one first if it is available.

This means your laptop will, from now on, always use ethernet where available in preference to WiFi and makes turning the WiFi off redundant in most cases. 

No idea if this will help - just a suggestion...

That said, Windows should prefer a wired connection anyway.

With both connected, type 'route print' from a command line prompt. Check the 'metric' numbers and make sure that the interface associated with your WiFi has a higher number.

Steve - Thanks for the suggestions.  I tried that, but I'm afraid it did not work.  One thing I noticed with the "route print" command is that under Interface List, there are three connections listed:  Ethernet card, Wireless card, and Juniper Virtual Adaptor (even though JNC is not running).   I might try uninstalling JNC to see if that helps.  However, even if it works, it is far from an ideal solution since I would have to reinstall this every time I need to use it to access a remote server, and then uninstall it again to use SkyDemon without the launch-error-logout-relaunch-login charade every time.  It is a shame since SD is a great product, but thrashing around in the dark trying to resolve this by time consuming trial and error does rather take the shine off it.

Without going too deeply into how SkyDemon uniquely identifies your computer, it does involve the network interface cards installed. It might be that your VPN is changing something about itself each time your computer starts, or something, and therefore our server does not recognise your machine next time you go to connect.

Thanks Tim.  That does give a clue as to what to look for.  I will try uninstalling the VPN software prior to using Skydemon next time to see if that helps.  If it does, I will have to weigh up which I use most out of Skydemon or VPN in deciding how to proceed.  I would love it to be Skydemon, but alas flying does have to take second place to work...

Why don't you just log out of SkyDemon each time you've finished with it.

Logging out after every use is certainly one possibility, though it might take a while for me to remember to do that :-)
I have at last had the chance to test the option of uninstalling the Juniper Virtual Adaptor VPN software, and, fingers crossed, that does appear to do the trick.  I hope that helps anyone else suffering the same problem.  I now just need to decide which is less of a pain;  reinstalling/uninstalling the VPN software every time I use it, or logging on and off Skydemon every time.

You could write a little script which deletes your license.skdl file (under Documents\SkyDemon) which has exactly the same effect as logging out.