If a subscriber reports a missing confirmation message to you, there are two approaches you can take based on the time frame of the subscription.
Less Than 12 Hours After Their Subscription
Because often times the issue with missing confirmation messages is attributed to ISPs take a little longer than normal to put messages into the inbox and because sending additional confirmation message makes the link in the first invalid, there is a 12 hour period where no additional confirmation message can be sent.
For the meantime, you might suggest to the subscriber that they:
If after this period of time, the message still is not found, they may need to take additional measures.
More Than 12 Hours After Their Subscription
If the message is still not found after this period, your subscriber should:
Although most issues with the delivery of the confirmation message can be resolved through working with the postmaster of most email providers, the quickest and most straight-forward way to a solution is simply to have the subscriber use another address that likely will not carry the same issues.
If you haven't yet suggested this resolution, you might strongly consider doing so at this point.