I have done a new design using the LTC1732-8.4 to charge a Li Ion battery at 1.5A. My Rsense is 0R07 and my Prog is 19K6. I get absoutely no joy from this circuit. It remains out of charge mode. I does not even enter C/10 charge.
I do see a problem in the schematic of the LTC1732-8.4 which accompanies your post. Battery current is sensed as the voltage between VCC and Sense pins. Diode D1 will interfere with the voltage seen between the 2 pins. Remove the diode so that R16 will be placed directly from VCC to Sense pins.