Ah yes, whenever you edit a path, the rotation center automatically goes back to center. I don't really know why that happens.
I can think of a couple of possible solutions. One is that before you edit the path, duplicate it. Then after you edit the path, you can snap the rotation center to the rotation center of the duplicate. After that, you can delete the duplicate.
Or another idea is before you edit the path, drag out 2 guides, one horizontal and one vertical, and snap them to the rotation center. Then after you edit the path, you can snap the rotation center to the guidelines' intersection.
I might have another approach for you though. From the image you showed, it reminds me of this tutorial for drawing a tachometer. So this is just in case it might work better.
http://goinkscape.com/how-to-create-a-tachometer-in-inkscape/