Okay, having been a boxer back when I was young and in the military, and now being a long term Aikidoka, and BJJ student, I think I might offer some perspective. Aikido isn't designed for sparring. I'm sorry, it just isn't. Here's why. Aikido NEEDS a committed attack. If you are not willing to step into your punch and commit, I can't affect your kuzushi and/or disrupt your center. It's ancestor worked great on the battlefield, where soldiers committed to their attacks (often with weapons). Aikido works well against the guy in the bar who just took a full swing at you with a pool cue....or the guy trying to smash you in the face with a bottle. One on one against a trained fighter? Not the best choice. Here's the thing. NO art is perfect...none. In a one on one sparring/sporting match, BJJ, Judo, Wrestling, Boxing, MMA, are all far, far better choices than Aikido. But how about against multiple attackers? How about against weapons? In Aikido we always, ALWAYS assume 2 things. 1. The attacker has a weapon....it could be a brick, a baseball bat, a knife, etc., we assume they have something. 2. They have friends. It won't be a one on one fight. In those situations, not that they are ideal for ANY martial art, Aikido is probably a better choice than any of the above...why? Because we actually train against multiple attackers, and against weapons all the time. I've been training BJJ for awhile now as well....have never trained for EITHER of those things in BJJ.
So, if a boxer wanted to probe and throw some jabs....a real Aikido practitioner wouldn't do anything...they would just back up out of range, and wait for the boxer to step in and commit. Which won't work well. It's akin to asking why your championship rally car isn't able to race against formula one cars on a formula one track and win? Different arts with different purposes. YMMV.