Generally speaking, it is better to close your database connection and recordsets as quickly as possible because they use server resources. Not much, but when lots of users are connected it could make a big difference.
In your case, I would keep the connection open, use a separate object for each recordset. Don't create the recordset object until you are ready for it, then close it as soon as you are done with it. Create the next recordset object, use it, close it. And so on.
Hope it helps.
-George
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