Sounds like a faulty TDC sensor. Could also be oil contamination in the connector (this is typical of Honda's that have oil leaks on the back of the engine). Oil tends to run down and eventually contaminate the crank position sensor connector causing intermittent signal. The car can drive with the issue in OPEN LOOP mode but will operate in a reduced performance.
It could also be the CKP sensor in the distributor. You will need to test the circuit on both with an oscilloscope to ensure the sensors are putting out the correct voltages when they rotate. Compare the maps to the Honda Service manual to ensure the maps are identical. if the voltage maps are different then the sensor is bad.