I have a meeting I need to run to but this thread I found may have some useful information in it.  I will keep digging when I get back as well.

https://forum.ethereum.org/discussion/5195/riser-1-to-3-pci-e-1x

Edit 1:

After reading through the above thread and taking a look at Intel's specs on the h81 and z87 it would appear that the max PCIE lanes through the h81 chipset is 6, whereas the z87 chipset can handle 8.  The 1x PCIE slots run through the chipset, but the 16x slot runs straight to the CPU. 

I would think that you could run 6 GPUs max through the chipset while running the remainder of your GPUs through the 16x slot using the CPUs remaining availability. In this scenario you could only ever use a 1x2 card in one of your 1x slots.  If you moved the 1x3 card to the 16x slot then you could run 5 GPU through the chipset and 3 (or more depending on CPU, driver, OS) through the 16x PCIE straight to the CPU.

But that doesn't seem to be your experience.  If you have the 1x3 card in the last 1x PCIE slot then the 7th card you plug in should be the 6th card running through the chipset.  Theoretically you should be able to run 7 cards with your setup, but not 8.  And you can't.

So I'm wondering, perhaps we have a bottleneck somewhere else?  Out of curiosity, what CPU are you using?

http://ark.intel.com/products/75013/Intel-Z87-Chipset

https://ark.intel.com/products/75016/Intel-H81-Chipset