Are you putting breakpoint at the line:
if(uartRxDataWrReq->handleValPair.attrHandle == CYBLE_SERVER_UART_SERVER_UART_RX_DATA_CHAR_HANDLE)
in app_UART.c file of the peripheral project, and finding that for one byte sent from central, multiple times this line is serviced?
My Problem was that I did not understand how tera term functions, one byte at a time. I was thinking that typing a series of characters into the window would result in those characters being stored in a fifo, irrespective of the breakpoint occurring, so that all characters could ultimately be accessed. But this is not the case. The breakpoint stalled the transmission of subsequent bytes of data, so I went instead to a terminal program called Cool Term which allows you to transmit an entire string at once, and I was able to access all bytes that were transmitted.