After reading this lengthy description several times, I doubt that a long-term solution to these recurring problems will be easy, even if it is possible.  What you describe is a series of fatigue failures as represented by cracks occurring at the weakest section.  The corrosive nature of the chemicals will contribute to fatigue failures in most alloys.  The best that can be done is to analyze each failure to decide if a specific factor is a major contributor to the failure and then attempt to reduce the effect of that factor.
 
The first step should be an attempt to reduce the weak spots in the mixer and baskets.  The second step should be to examine welds, to be sure that they do not undercut the base metal, contributing to a stress riser.  Then look for possible trace materials in the reactants, to be sure that some secondary chemical, like a dissolved salt, is not accelerating corrosion.  Finally consider alternate alloys or alloy suppliers to decide if a better material is available.
 
I do not think you will find a magic answer to your problems.

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