just a few experiences of mine on the original subject (BJJ attack and Aikido defense):
I started Aikido in a dojo where the sensei was teaching Aikido with quite the fighter mentality as he was an experienced fighter himself, and thus he valued what he called "effective" techniques over "pure" aikido techniques. This way a lot of karate/judo elements were incorporated in our training. Now, despite his preference to the "effective", he held Aikido principles in the highest esteem, so we were still doing Aikido, even though it was augmented with judo/karate elements. That was until we met BJJ. Then we began playing around ground fighting/grappling, and a slow, painful process began as we saw all our beloved Aikido techniques proven useless against this new fighting style. Eventually the entire dojo were converted to BJJ.
We were trying a lot of things, but basically if you are fighting with a Aikido against a grappling opponent, you have to feel distance and positioning extremely well, atemi is a must, you need to utilize your center very precisely - all in all you need to do aikido at a very high level, and even then, you will not get away unless you have a good knowledge on how a takedown works. And that is, if your opponent is at a beginner level. With more experienced BJJ grapplers things can get exponentially worse.
BTW the only "official" aikido technique I saw against tackling was this (performed by Osensei):
PS: some early post mentioned ki aikido exercises as a possible counter for takedowns. Sadly, in my experience, they wont suffice. Unbendable arm wont save you from armlocks nor will unliftable body prevent you from being taken down. They work fine against forces with constant direction and intensity, but against spiralling or "jerky" grabs where the opponent can change the direction of the force any time, they wont work, or it would require an extremely high level of skill to make them work.