I think you should probably separate resignations during the term from resignations in the last year or so. In the last year there are usually a lot of resignations as Cabinet members move on to new jobs.
I haven’t been able to find much about this online, but I believe it was FDR because of the sheer amount of time he was in office as well as the number of positions he created as president.
@hossman: right you are; people probably move on in anticipation of the end of the term, though presumably this would be relatively uniform across presidencies.
@skwerl88: by “in a given term,” I did mean to make total “time in office” irrelevant…but your observation is well taken that the number of cabinet positions that a president creates probably has as much to do with the number of tendered resignations as does his popularity among his inner circle. (And yes, I use the masculine pronoun advisedly.)
The thrust of the question, I admit, was to see if it wasn’t good ‘ole W…since he’s so historically unpopular with “we the people.” But probably you’re right that it’s somebody like FDR who more hugely expanded the cabinet.