Any fix for PLA prints getting more brittle over time?
PLA absorbs moisture, so keeping the filament dry is a key factor. Aside from that, PLA is naturally more brittle than other plastics like ABS and Nylon Sorry, tried to find a graph to prove it, but couldn't find one.

There's a good Google Group discussion and many other resources that go over good storage habits, but as for fixing the existing filament.

Try the following: 


Place PLA in an enclosure (plastic bin, Zip-loc bag, etc.)
If you have some, add some moisture absorber(s)
Place the tub in a warm environment (naturally or artificially) and make sure the area is dry as possible (not in the shed in the back, by the woods...). Possibly next to a heater vent or space heater in your house?


Essentially, you're trying to treat the material. When the material goes through a heat treatment (aka the heat block in the extruder), the mechanical properties are beginning to change. The brittleness can be set by how quickly the material cools. I'm speculating that the moisture does any of the following:


Keeps the filament from heating up to the desired extrusion temperature.
Burns the filament.
The moisture is evaporated, leaving gaps in the extruded filament (under microscope).


I looked into this a few years ago and have forgotten most of what I found out, but I'll keep looking and update my answer here.