Handling Log File During Data Import

Hi,
i have a package that uses a ForEach loop component to import flat files, and uses an OLE DB Destination component to insert the data into some staging tables (using table fast load with a max insert commit of 1000 rows), the biggest individual table import would be circa 5000 rows. At the end of each file import a stored proc is called to transfer the data into production tables, then the next file is imported.

Periodically (when importing more than 5 or 6 files) the process fails with the error message:

The transaction log for database 'blah' is full. To find out why space in the log cannot be reused, see the log_reuse_wait_desc column in sys.databases

This occurs when committing the data to staging. I do not start any transactions during this process, and the staging tables are cleaned out by truncating them, so i'm not sure exactly what is causing the log file to fill up (i'm not a DBA).

I know this is not specifically a SSIS problem, but can anyone give me a suggestion about the best way to handle the log file during an SSIS import? Should i execute a DBCC SHRINKFILE before each flat file is imported? Is there some other approach i should be taking to either insert the data or to move it from staging to production?

Thanks!