Laura,
Thanks for a good question regarding maximum age in SS.
SS treats the maximum age, max-age, as an accumulator age, so it need not be the oldest fish ever observed.
It is important that there be little change in age-specific dynamics beyond the chosen age. If you are modeling growth and using length composition data, then it is best if fish are close to Linf as they enter this age, although SS does have algorithms to deal with growth within the maximum age. It also is important that selectivity is not changing because SS will assign the same age-specific selectivity for all fish in this maximum age. Ageing error is another factor to consider. SS will assign all fish in max-age to the same distribution of observed ages; it will not know that the theoretical very old fish within the max-age bin probably will be read as being older than a fish that is barely old enough to be in that bin. So there are plenty of good reasons to make max-age fairly old, but that is countered by the sparseness of data for old fish and the fact that SS will run slower the more ages it needs to deal with.
I hope this helps. Perhaps some other folks can relate their experience with selecting max-age.
Richard D. Methot Jr. Ph.D.
NOAA Fisheries Senior Scientist for Stock Assessments