Shay,
FYI, you are asking a question about ArcMap within a forum related to a different product, ArcGIS Explorer for Desktop, so you might get more answers if you posted in a forum about ArcGIS for Desktop (ArcMap is part of that suite).
Jayanta is correct, you cannot perform a one to many join in ArcMap.
What you are experiencing is not a flaw of ArcMap, it is a result of trying to perform a one-to-many join, meaning you have one geographic feature (your polygon), and you are attempting to join many records to each feature. ArcMap will just take the first record it comes to and this will be the only one showing in the table.
Other than using a relate rather than a join, here are some other paths you might consider.
Some other options would be to aggregate your data before joining as a one-to-one; in Excel you could create a pivot table such that the row should be the attribute you are joining to the polygon, then summarize the relevant information such as taking a count, the mean, or the sum of other attributes, then join these results to your polygon. This will be a one-tone relationship, because there is one row of information that you are joining to one polygon.
Another path which might work if your 6615 records have point based coordinates,plot them with their respective X,Y locations then do a spatial join, such that the polygon attributes are added to each record (point). This would be a many-to-one join.
Hope this helps,
j