Tiny spots on avocado leaves (indoors)

[cruiserandmax]

I had a bunch of avocado plants grown from pits that started developing tiny dots like this. Eventually the leaves with the brown dots start to die- but it takes a long time- long enough so the plant doesn't seem to die altogether, but just loose leaves at the rate that it grows them...

Can anyone recognize these spots. And any ideas on how to get rid of them, or stop them from spreading onto new leaves?

 

[cruiserandmax]

Also on the off chance it is relevant- we have cats that are constantly investigating/touching the leaves and soil in these plants.

 

[cruiserandmax]

Well, I just covered all the leaves with Neem oil. I'll see how that goes.