If an auto message (or any custom-text message) didn't go out to an Amazon buyer, this is usually Amazon blocking the message on their end, not a problem with the Auto Messages tool itself.
Amazon controls which messaging options are available per order through their Buyer-Seller Messaging API, and custom-text messages aren't always available - so an auto message can be skipped or fail to send even when the automation itself is working correctly.
This is expected, policy-driven behavior on Amazon's side. Amazon may block custom-text/auto messaging for a specific order if:
The order is in a stage where custom messaging isn't allowed (for example, certain pre-shipment or post-delivery windows)
The messaging window has expired (commonly 30+ days after delivery)
The seller has hit the maximum number of messages allowed for that order
The buyer has opted out of receiving seller-initiated messages
The seller's account has past messaging policy violations or restrictions
This can vary by order type (FBA vs FBM), by marketplace, and by where the order is in its lifecycle - so an auto message may go through on one order but not another, even under the same automation rule.
If no custom-text option is available for an order, there is currently no alternative way for the auto message (or any manual message) to reach that buyer through Amazon. Sellers should check that the order still falls within Amazon's allowed messaging window and hasn't exceeded messaging or policy limits.