Could be a timing issue.
I can't tell which are Select queries and which are Action queries, but maybe try this:
Code:
Private Sub BtnOIG_Click()
Dim d As dao.Database
Set d = CurrentDb
'Import Monthly OIG Spreadsheet
DoCmd.RunSavedImportExport "Import-SoinMonthlyOIGDownload"
'Determine new volunteers
d.Execute "QselMonthlyOIG"
d.Execute "QselNewMonthlyOIG" 'Unmatched records with TblPermOIG"
'Add new OIG to TblPermOIG
d.Execute "QappNewOIGToPermOIG"
'Prepare OIG for export to Excel
d.Execute "QdelTblTempOIG"
DoEvents '<<--
d.Execute "QselNewMonthlyOIGForExcel" 'Selecing required fields'
d.Execute "QappNewOIGToTblTempOIG" 'Table has required names for Export'
DoCmd.RunSavedImportExport "Export-Soin_MonthlyOIG"
MsgBox "Monthly OIG has been exported to Excel"
DoCmd.Close
DoCmd.OpenForm "Volunteer Menu"
End Sub