Are any of the subreports "On Demand" subreports? If they are, then they have to connect to the database when the user wants to see the subreport - there is no way around this unless you turn off the "On Demand" feature.
One other thing you may want to look at doing is schedule the report to PDF output instead of to RPT. This will guarantee that all of the non-On Demand data will appear in the output.
-Dell