One reason you might get unpredictable results with:
{ IF {MERGEFIELD Member_} = "503*" {INCLUDETEXT "Epsilon - Syracuse University"}
{ IF {MERGEFIELD Member_} = "562*" {INCLUDETEXT "Beta Tau - University of Florida"}
{ IF {MERGEFIELD Member_} = "571*" {INCLUDETEXT "Gamma Zeta - Northern Illinois University"}
is that you've omitted the file paths. These should be included, with double backslashes for the separators. For example:
{ IF {MERGEFIELD Member_} = "503*" {INCLUDETEXT "Drive:\Path\Epsilon - Syracuse University"}
{ IF {MERGEFIELD Member_} = "562*" {INCLUDETEXT "Drive:\Path\Beta Tau - University of Florida"}
{ IF {MERGEFIELD Member_} = "571*" {INCLUDETEXT "Drive:\Path\Gamma Zeta - Northern Illinois University"}
Another possibility relates to your use of *. That is a wildcard and tells Word to output the same
INCLUDETEXT field for any Member whose designation matches the first three digits, regardless of how many characters follow those first 3. Thus, if you had:
{ IF {MERGEFIELD Member_} = "503*" {INCLUDETEXT "Drive:\Path\Epsilon - Syracuse University"}
{ IF {MERGEFIELD Member_} = "5035" {INCLUDETEXT "Drive:\Path\Beta Tau - University of Florida"}
you'd get both letters for any Member whose number begins with 503. It might be worthwhile including the
{MERGEFIELD Member_} field in the mailmerge main document on its own so you can see what it's outputting with the problem records.