I can see a customer's charge failed in my Stripe dashboard, but received no email alert. Why has this happened?

Stripe will show a failure when any payment to your Stripe account fails, so this would normally happen because a customer has failed to make a booking where the payment due now. Because the payment has failed, usually because the card was declined, the booking has not been made and we would not send an email alerting you to the failure.
Where a customer has made a booking for staggered payment (i.e. where the due date occurs after the booking date), a payment failure will result in a payment failure email from Pitchup.com.