In the case of SaaS type software you can be sure of one thing: the administrator can always count on users informing him about failures.
But you have to admit that it is better to avoid such situations. You cannot prevent failures but you can minimize the time in which they are eliminated by ensuring they are found the moment they start.
Your application is exceptional and unique. Standard monitoring services will not be able to monitor anything more than its availability and failures can be very different.
But do not worry - you can still count on external monitoring that it will inform you about every failure before users notice it. You simply need a dedicated solution which is based on mechanisms adjusted to the functionalities and processes of your website.