You can do it automatically through a number of ways.
1. If your DB is SQL Server you could set it up in a SQL job (I am sure other server DBs such as Oracle have similar functionality, but I am not aware of it).
2. You could store a date with the IPAddress and in your code check if it is past a week. If so, change the date and allow the query to continue, otherwise abort the process.
3. Assuming you are on a windows platform (a fair assumption for ASP) you could use a windows scheduled task to execute a script and delete from this table. Similarly, you could set up a service to do the same thing.
I am sure there are many other ways, but these are the first three that come to mind.