So, the only way I've gotten the scissor test to work is by calling flush immediately after I draw the sprite, but this wouldn't work with my text objects (on account of the ID3DXFont interface not allowing you to prematurely flush the text to the screen, unless there's something I'm missing), so this isn't a sufficient solution.
From what I recall, you can pass in a ID3DXSprite-Pointer to the ID3DXFonts draw method, in which case flushing the text will be drawn in respect to the sprite - you'd want to do that anyway, since it will speed up text rendering, and it should also fix your issue. Unfortunately there really is no other way then to flush whenever you change the clip rect. The only way around it would be to implement your own sprite renderer with a software clip rect, but this tends to be slightly slower than the hardware-equivalent. Yet, if doing so enables you to draw ALL sprites like from your gui in one draw call instead of multiple ones needed in case of the ID3DXSprite, the price might be well worth paying and can actually result in a speedup.
Oh wow. I was already passing in a ID3DXSprite pointer to the ID3DXFonts draw. I guess I didn't put two and two together and realize that it was doing that to actually draw the text =P. I guess I'll just flush every time I need to scissor clip these things. Thanks for the answer, it's working now.