Filemaker odbc is an old implementation of the odbc api and is not really optimized to allow communication with a web server that open many connections to the database.
If you need to build web site using Filemaker and IIS you should take a look at Blueworld LASSO or JSP
It sounds like you're trying to publish FMP data on the web using ASP. Using ODBC to connect the two is not a good idea because FileMaker's ODBC is too slow for a web server.
Instead use http/xml to transfer data back and forth between ASP and FileMaker. You can use the MSXML http object (provided by MDAC) to send http requests to FileMaker from ASP. If you specify an xml format file from FileMaker (like fmp_xml or dso_xml) in your http request, then the MSXML object will return an XML DOM you can walk with your JScript or VBScript code. This is much, much faster than retrieving data from FMP using ODBC.
Alternatively, you can use PHP to do the same thing. The difference is, Chris Hansen already wrote an object class in PHP that handles the HTTP query building and XML parsing for you. You can download his free code at www.iviking.org. Also, Steve Lane from The Moyer Group has written a good white paper about it at www.moyergroup.com under "published works".