as suggested by San Bergmans tie those signals and i have noticed in my earlier application that qbasic was not fast enough to handle the communication.
you may have to increase the receive buffer(RB) size. alternatively you can clear (read) every byte as it is received. i have given the com port initialisation from an old application
ignore unneccessary paramaters from the below line

Open "COM2:9600,N,8,1,CD0,CS0,DS0,rs,RB2048" For Random As #1

use help menu on the qbasic to know about individual parameter.