Can all separate rerandomizations be saved separately?

There are at least two interpretations of this question.

a) I want to show several of the graphs or tables that result from rerandomization.

Select the graph or table and choose Copy Picture from the Edit menu. Deselect everything in the document (click in a blank area) and choose Paste Picture from the Edit menu. This will give you a static picture that will not change when you next rerandomize. Repeat as many times as desired.

b) I want to compute something each time I rerandomize and save the results of these computations.

Do your computation as a Measure in the collection's Inspector. (You can have as many Measures as you want.) Then use the Collect Measures command in the Analyze menu to repeatedly rerandomize and collect your measures. Each rerandomization will be one case in the resulting Measures Collection, with each measure an attribute.