Watching the chi2 value is the logical thing to do. And if the value increases between iterations, then it is logical that alarm bells should ring. Without creating statistics or parameter counts for each iteration, it can be hard to tell that the increasing chi-squared value is correlated with a massive collapse of model complexity.
On the other hand making the leap to watching the AIC value, from the statistical point of view of model selection, I would say is illogical. It's only if you think of the AIC value as an approximation to the discrepancy, a measure of lack of fit, that it then makes sense to follow that value over the iterations. It also doesn't help that a written description of these concepts is missing from the 'full_analysis.py' script! Optimising parsimony to obtain the model-free results is a bit of a new concept.
Edward