In order to connect to a named instance of SQL Server you will need to configure an alias for that instance as described here: http://support.microsoft.com/kb/265808
That will allow a direct connection to that alias from the HelpSpot Windows installer.
In extremely rare cases SQL Server can lose seeding on the HS_Request table or another tables, primary key. If this occurs inserts to the database will fail with this error. You can check if this is the case by running the following in management studio:
DBCC CHECKIDENT ('HS_Request');
If the current seed value doesn't match the current column value (it will be less) than there's a problem. You can reseed the tables primary key with this command:
DBCC CHECKIDENT ('HS_Request',RESEED,######);
where ###### is the new ID value. Make this a few higher than the current highest value in the table. That should resolve the issue.