Customer did pay, I can find his details in the Mollie-administration but the order is not visible in Bakery in the back-end.
These kind of problems typically happen when the visitor is taking a long time between the start of ordering and actually paying.
Bakery clears unfinished orders after some timeout (to give back any reserved items). In the current version it is a 1 hour timeout. The fun part is that this clearing is only done when another order is started, so on low-traffic websites this problem is less likely to happen.
The PHP session could still be active - holding the ordered items - and the payment process could still be done by the visitor. The payment notification however cannot be linked to an order anymore.
The result is that no confirmation/shop emails are sent, and nothing about the order can be found in the backend anymore.
If you have access to the webserver logs, and know what time the order went wrong, you might be able to find this caused the problem.
There is no real soution for this. You could change the timeout to a much longer period causing products being reserved for a longer period (if you use the stock functionalty).
In Bakery 1.7.8 it is done in view.php.
Line 191 sets the timeout to 60 * 60 * 1. (the value in seconds)
Setting this to 60 * 60 * 3 will allow the visitor to wait between order and payment for 3 hours.