Does the fridge actually matter or is that just caution?

Every source says refrigerate after reconstitution. Is that a real stability issue or the usual err-on-the-side-of-caution advice?

Real, and the mechanism is not mysterious.

Dry, the peptide is fairly inert — there is very little water around to react with it, which is the entire reason things get freeze-dried in the first place.

Once you reconstitute it you have put it in solution with the reagent that degrades it. Hydrolysis cleaves the backbone; oxidation goes after particular residues, methionine, cysteine, tryptophan; and both go faster when warm. That is chemistry, not caution.

The storage post has the detail. Short version: dry and cold is stable for a long time, wet and warm is a clock.

The corollary nobody mentions is that you cannot see any of it.

A degraded peptide solution looks exactly like a fresh one. Clear, colourless, no smell. There is no point at which it announces itself. So the sequence is: it stops working, you conclude the compound does not work, and you were actually testing a vial that had been sitting in a warm room.

Which is one reason self-reported "did nothing for me" is such weak evidence in both directions.

Yes — and the reverse of that, which is the one that gets people hurt: visible cloudiness or particulate means something has definitely gone wrong, but clear means nothing has visibly gone wrong. Absence of evidence.

Freeze-thaw is the other one. Every cycle costs you something, and "I will just put it in the freezer to be extra safe" is a common and counterproductive instinct.

Aliquot it once if you are going to freeze anything, rather than thawing and refreezing the same vial six times.

Salient detail from the same post that I nearly missed: the fridge door is the worst place in the fridge. It swings through the largest temperature range of anywhere in there, several times a day.

Which is of course exactly where everybody puts small vials.