The problem with calcium sulfate is the presence of water.  I'm assuming they have some. But even without water, the solids are very fine and do not filter well. The second problem is the time for reaction. If the reaction is rapid, the calcium sulfate would come out as sub-micron particles with 1/2 water of hydration.  The chemical wants to be the 2 water of hydration form.  Also, some sulfones will co-precipitate with the sulfate as inclusions that bring along water to complete the hydration. The filter press may not be the best dewatering device since the pressure promotes the formation of the finer particles. I've seen better results with a centrifuge. 

This will increase throughput of the dodecylbenzene product. The slurry can be filtered to capture more of the product (more economics rather than process requirement) in the filter press, which is  probably limited by liquid throughput rate. Other options may be the seeding of the feed to the filter with calcium sulfate-2 H2O (this requires more equipment and process control than a centrifuge). The impurity (sulfuric acid) may be better removed with magnesium hydroxide and then re-slurry, washing with calcium hydroxide. There are several other chemical inversions that could be applied depending on the ultimate requirements or usage of the calcium dodecylbenzene sulfonic acid. Usually liquid-liquid extraction is better for this class of organic acids.