Check the card's Email Delivery line:

• Scheduled for … Pending — a future Delivery Date was chosen; the email is sent by the scheduled job once that date/time passes (only for cards that are still Active and have a recipient email). Click Resend Email to send it right now instead of waiting.
• Sent immediately but no Sent badge / empty Sent to — the buyer left the recipient email blank, so nothing could be sent; add an Email To Send address and click Resend Email.
• Card is Cancelled — the scheduled job only sends for cards that are still Active, so a pending send is skipped once the card is cancelled.

If the badge already says Sent, ask the recipient to check spam; the email comes from your configured sender and uses the "user_giftcard" system email template.