We experimentally demonstrate a single-shot arrival time monitor for short picosecond infrared freeelectron laser (IR FEL) pulses based on balanced optical cross-correlation with a synchronized fs table-top laser. Employing this timing tool at the Fritz Haber Institute IR FEL, we observe a shot-to-shot timing jitter of only 100 fs and minute-scale timing drifts of a few picoseconds, the latter being strictly correlated with the electron beam energy of the accelerator. We acquire sum-frequency cross-correlation data with micropulse resolution, providing full access to the IR FEL pulse shape evolution within the macropulse. These measurements provide unprecedented insights into the occurrence of limit-cycle oscillations of the FEL intensity as a consequence of subpulse formation. Our experimental results are complemented by fourdimensional simulations of the nonlinear pulse dynamics in a low-gain FEL oscillator based on MaxwellLorentz theory.