Why the record disappears
A review invitation arrives by email, you accept, you submit the review through a portal, and the thread is archived or deleted. Two years later the reviews exist and the proof does not.
Peer review is confidential by design, which compounds it. You generally cannot share the manuscript, the report, or in many cases even the fact that a specific paper was reviewed by you. What you can evidence is that you reviewed for a journal, and how often.
Changing institution makes it worse. Invitations sent to an old university address become unreachable the moment the account is closed, which is exactly when people most need the history.
Reviewing is confidential, so the only evidence is what you kept at the time. It is close to impossible to reconstruct later.
What to keep, starting now
A running log: journal name, date of invitation, date the review was completed, and the manuscript identifier. A spreadsheet is entirely adequate. This takes about a minute per review.
The invitation email and any completion or thank-you acknowledgement, archived somewhere you will still control after changing jobs — a personal address, not an institutional one.
Use a verified reviewer platform where the journal supports it. Several publishers and independent services record completed reviews and can produce an exportable record, which is far stronger evidence than your own log because it is third-party.
If you have reviewed in the past without keeping records, ask now. Many journals will issue a confirmation letter on request, and they can do so much more readily for a recent review than an old one. Editors and editorial systems change.
Where the record gets used
Promotion and tenure cases routinely ask about service to the field, and reviewing is the most common form of it. A documented record answers the question; a vague claim does not.
It matters most in evidence-based immigration assessments. Judging the work of others is one of the ten EB-1A criteria and appears in the O-1A list too, and there the evidence has to be documentary — an assertion that you have reviewed is not the same as proof that you did.
Editorial roles belong in the same log: guest editing, programme committees, grant panels, thesis examining. These are all judging the work of others, and they are all easier to evidence contemporaneously than in retrospect.