The rationale for having each item show at minimum 500 times and preferably 1000 times was laid out by Rich Johnson (our founder) back in the 1990s when describing quick-and-dirty sample size calculations for CBC. But, the same logic applies to MaxDiff.
The reasoning behind the target of getting 1000 exposures of each level of an attribute in a choice experiment was that in aggregate analysis (and doing Express MaxDiff typically involves aggregate analysis) allowed one to obtain approximately +/-3% margin of error on the counts (win rate) proportions. 500 exposures allowed one to get about +/- 4% margin of error. MaxDiff is a different animal than CBC analysis, for which this original quick-and-dirty sample size calculator was proposed...but it is a handy approach to think about as a first cut at sample size thinking.
We discuss this quick-and-dirty counts-based sample size rule in our book, "Becoming an Expert in Conjoint Analysis". It is also referenced in our book, "Getting Started in Conjoint Analysis".
But, question for you, why use Express MaxDiff? We tend to prefer Sparse MaxDiff for situations involving a large amount of items in MaxDiff. It has proven multiple times in our simulations and our checking with real respondents to perform better than Express MaxDiff.
And, if the principal goal is to identify and measure the top few items, then Bandit MaxDiff is about 2.5x more effective (efficient) than Express or Sparse MaxDiff when dealing with 80 items, and 4x more efficient when dealing with 120 or more items.