Accepted answer
Nobody has published a cycle count, and at 5 mg/mL the concentration tells you what a wrong guess costs: a 0.1 mL aliquot holds 0.5 mg and every microlitre is 5 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 5 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 5 mg/mL and the date, and never thaw a container you will refreeze.
The part that matters: buffer components crystallise at different rates during freezing, which shifts pH locally by a surprising amount.
Buffer salts crystallise at different points during freezing. Sodium phosphate is the classic example: the dibasic form crystallises first and the pH of the residual liquid falls by several units. That pH excursion is the real damage in many cases.
The mitigation is aliquoting. Divide the reconstituted solution into single-use volumes before the first freeze, and each aliquot then experiences exactly one cycle.
Selective crystallisation of sodium phosphate buffer components producing large pH shifts on freezing is a classical result in the lyophilisation literature.
Aliquoting itself is a handling step and introduces its own contamination opportunity.
Let a frozen vial reach room temperature before opening, or you condense water into it.