Finally found it. It was a problem when accessing the database to update some data that was buried several methods deep. I forgot to close an IBM.Data.DB2.iSeries.iDB2DataReader object after using it to get a schema table.
Dim rdrSchema As IBM.Data.DB2.iSeries.iDB2DataReader
Dim cmdSel As New IBM.Data.DB2.iSeries.iDB2Command
cmdSel = inDaFile.SelectCommand
rdrSchema = cmdSel.ExecuteReader(CommandBehavior.KeyInfo)
dtSchema = rdrSchema.GetSchemaTable
rdrSchema.Close()
Thanks to those who suggested possible problems!