Sorry I was out with the flu. I was worried about this topic the whole time! But I'm glad Moini seems to have a better idea about this, than I do. It's starting to sound like there might be a bug (in Inkscape)....or maybe not so much of a bug, but maybe just that Inkscape hasn't caught up to that technology yet.
Just for my own info -- If the tablet has its own operating system as well as Inkscape installed, why do you need the PC anymore? What role does the PC play?
And so, when you're drawing on the screen of the tablet, are you also drawing directly onto the Inkscape canvas?
The last time I tried to learn about graphics tablets, I was told you couldn't see what you were drawing on the tablet, that you could only see it in Inkscape, on the PC screen. So things have changed apparently.
It was at that time that I learned some weird things can happen if you rest the PC mouse on the tablet. That couldn't be the problem, could it?
Did you say this is happening eventually with all files? Or is it just one file? Is there anything else in the files, besides your Calligraphy (such as imported raster images)? A sample test file which shows the problem would be helpful. Even if the problem is happening in every file, there still could be something you just didn't think of. Like for example, do you use a custom default template?
I wonder if the Input Devices dialog (Edit menu) might have some helpful options? When you said how you can scroll away to clear the screen, and then scroll back, it seems to temporarily fix it, makes me wonder. I don't understand much about the Input Devices dialog, but the Mode dropdown menu seems to have options which define the active area. Maybe it needs to be set to the Window? Maybe if it's trying to consider the whole screen, it's too much for inkscape? Or maybe it's the other way around? I see there's an option for pressure sensitivity there. So if it's not checked, you could try it.
It probably has nothing to do with it. But it would just take a moment or 2 to try it.
Edit
I was just checking on the control bar, since I don't use that tool very often. If you're using a preset style, you could try not using it, just in a test file. Just select No Preset. Same if you're using a custom profile.