Accepted answer
Nobody has published a cycle count, and at 2.5 mg/mL the concentration tells you what a wrong guess costs: a 0.1 mL aliquot holds 0.25 mg and every microlitre is 2.5 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 2.5 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 2.5 mg/mL and the date, and never thaw a container you will refreeze.
Answer first: each freeze-thaw cycle costs something through aggregation and pH shift, so the mitigation is aliquoting rather than choosing a better freezer.
Never refreeze a thawed aliquot. The whole point of aliquoting is that the aliquot is single-use, and refreezing it discards the benefit.
To be exact about it, the mitigation is aliquoting. Divide the reconstituted solution into single-use volumes before the first freeze, and each aliquot then experiences exactly one cycle.
Cryoconcentration of solutes at the ice front is a well-documented mechanism in freeze-thaw damage to proteins and peptides.
Aliquoting itself is a handling step and introduces its own contamination opportunity.
Aliquot before the first freeze. That is the whole answer.