And what does that "on Close script do?"
The On Close script does this:
1) Checks the value of a Summary field. The Summary field is tied to a boolean calculation field that error checks the record's related line items. If there is a problem, the user is prevented from leaving the record.
2) Runs another script that extracts certain data from the record and stores it in another database.
#1 is obviously a red flag; however, the database in question never closes, even if no data entry has occurred since the database was opened.
Just to confirm your suspicions, if you temporarily disable this script, does it then close?