We describe a highly sensitive and stable quantum-cascade laser-based attenuated total reflection (ATR) terahertz sensor for the detection of very low concentration solutions, using a dual-modulation differential approach and ATR geometry. This sensor offers a very high dynamic range and a long-term stability of 40 dB, which extends the potential of terahertz radiation for the analysis of liquid and biological samples. The performance is illustrated by measurements on standard solutions of ions, sugars, and proteins, for concentrations down to 1 M.