The pound signs (#) in the sequence number indicate an overflow on any DynaPath control. Based on this fact, and that there is no issue with the program file you are trying to send, there is a problem with the transmission of the program to the CNC.
Buffered Input, or drip feed, allows programs of unlimited length. There is no time out or sleep mode in Hyperterminal.
The description of the problem would indicate that the sending computer is not seeing the XOFF character sent by the control to pause the transmission (if software control is selected) or does not see the CTS (Clear To Send) line go low (if hardware control is selected). This could mean a problem with either the cabling or there has been a hardware failure on the UART in the control.
There is a small chance this is a software error that was found on Delta 20 controls shortly after the Buffered Input feature was implemented. If a sequence number just happened to start on a memory page boundary, a fault would occur. Please call DynaPath with the software level to check. The software level is given on the first screen to appear after booting, before you press the Mode Select key. It is a four digit number preceeded with a 'P' and possibly another letter (i.e. PA5203).
One way to get around this problem without updating the software is to vary the length of the blocks by adjusting the sequence numbers (using 3 digit sequence numbers instead of 4).