Right, after a morning spent slaving away over a hot spit roasting a ton of animals I don't even want, lol, these are the results;
Basically all small animals are affected with the exception of Magpies and Ptarmigans, both of which have no issues.
Rabbits, Squirrels, Adders, Chickens, Ducks and Swans all disappear on exiting the screen but, they all reappear on leaving again and returning, with the exception of squirrels, for me, squirrels never come back no matter how many times I go on and off screen. All of the others will go on and off on repeated exiting and entering.
They also all (again, not squirrels) will render if you turn the spit.
I haven't tested Moles or any of the larger animals as now out of time for the moment. Hope that helps.