What it sounds like is that the connections are not actually getting closed. While you are calling Connection.Close, it is entirely possible that it actually is not. I know some database drivers have a maximum number of open connections before they start raising a stink. It sounds like you're running into that wall.
Just for giggles, to try something out, see if the following code works in JavaScript
var connectionObject = Sys.OleObject("ADODB.Connection");
And then work through debugging your tests and make sure that your "close" call is getting called every time.