I've had similar issues when using DBD::ODBC. I fixed it by switching to DBD::ADO:

# for ADO usage
use DBI;
use Win32::OLE;
Win32::OLE->Option( CP => Win32::OLE::CP_UTF8 );

my $dbh = DBI->connect('dbi:ADO:Provider=Microsoft.Jet.OLEDB.4.0;Data 
+Source=some.mdb', '','', {LongReadLen=>100000} );
[download]

See the DBD::ADO documentation for more details, usage, and limitations.