Accepted answer
Nobody has published a cycle count, and at 20 mg/mL the concentration tells you what a wrong guess costs: a 0.1 mL aliquot holds 2 mg and every microlitre is 20 µg. Damage from freezing is not gradual attrition — it is concentrated at the phase transitions, where ice excludes solute and the unfrozen fraction climbs well above 20 mg/mL for as long as the transition lasts. Two slow cycles can therefore do more than four fast ones, which is why a cycle count is the wrong unit in the first place. The way to make the number one is to make it one: split at reconstitution into single-draw aliquots, label each with 20 mg/mL and the date, and never thaw a container you will refreeze.
On the detail: buffer components crystallise at different rates during freezing, which shifts pH locally by a surprising amount.
Thaw slowly at room temperature or in the refrigerator rather than in warm water. Rapid warming creates local thermal and concentration gradients that promote aggregation.
During freezing, solutes are excluded from the ice lattice and concentrate into the residual liquid. Local concentrations can rise many-fold, which promotes aggregation independently of temperature.
Aliquoting to eliminate repeated cycles is standard laboratory practice for exactly this reason.
Thaw slowly and never refreeze an aliquot.