The solar plexus is exactly a main goal in martial arts because there are basically no muscles above it that can be trained. The abs begin just below it, but well trained abs help to reduce the area that allows for critical impact there.
The solar plexus (or, correctly, celiac plexus) itself is a point where several nerves meet. A blunt trauma, like a punch, a ball, of just falling on you flat back, can cause these nerves to fire all at once.
The most common physiological consequence is a spasm of the diaphragma, resulting in what is normally described as getting winded.
So while improving core strength, training all the little muscles, and abs helps for hara in general (which just means stomach), there is simply no way besides having a guard and movement to secure this sweet spot. If you are hit there, you will lose some breaths. Overall physical condition and the level of conscious control over the diaphragma (as trained in the sanchin kata, as this beautiful video illustrates) may reduce the time of recovery up to the point that you can continue fighting, but as it is a direct neurological effect, there is no way of avoiding it completely.
Btw. core strength in general is not through crunches (rather than situps), this trains abs. You can look up some exercises for that here. One of the most basic ones is planking. The muscles trained in core training are actually not necessarily the abs, it is rather that training the abs is one part of core training. It is core for a reason.
To sum it up - the wisdom inherited in kata and basic body excercises routinely included in training in okinawan karate (regarding this, the video is worth a watch) is severely underestimated in western training.
