hyperterminal echo on
If you don't see nothing suddenly , then I bet that for some reason you stop receiving the echo in the port. There is also small chances to have other problems, like a broken key on the keyboard, deficient serial port, or program crashed, but check first the most obvious.
I suggest you: enable the local echo (this is a menu option checkbox in the HT), then you will see everything you type on the screen. So if you see a character 1 time means that the HT has see it from the keyboard (and probably transmit it) but nothing received. If you see 2 characters appear (like 'aa' when you type 'a') this means that one extra 'a' has come in the serial port Rx pin. If with enabled the local echo you still don't see anything on the screen, then you have internal problem. If you want to be 100% sure that what you type is transmitted, check the serial port's Tx with a scope (or even a multimeter) when you press a key. Also important to double check the communication settings and the wiring!