Why does the graph have a logarithmic shape? That is, why does the increase rate in %/hr decrease over time? The graph attached has a logarithmic line, but I can't figure out why. 
Does anyone have any potential justifications with respect to neuroscience?

Thanks!
A really satisfying answer would need a full account of what memory is and how forgetting happens, and the full story on that does not exist yet. But there's been some pretty solid progress since Ebbinghaus.

The first step towards an answer would be to nail down exactly what shape that curve is.
There's a careful look in:
Averell, L., &amp; Heathcote, A. (2011). The form of the forgetting curve and the fate of memories. Journal of Mathematical Psychology, 55(1), 25-35.

But the TLDR version is that the first-pass description of the shape as logarithmic is pretty ok, there's a power-law rule for forgetting. Interestingly the asymptote doesn't seem to be zero! So some elements of memory seem to be effectively permanent.

Why and how that works is a bit of a mystery. Averell and Heathcote cite 

Arshavsky,Y.I.(2006). The seven sins of the Hebbian synapse: can the hypothesis of synaptic plasticity explain long-term memory consolidation?

as discussing possible biological mechanisms for the results they found about the shape of the function, so that might be a nice place to start. But I don't think that's the last word on this! It's an ongoing research question.