Yeah, this is hard but so, so important!

There are three key items I would focus on:

1. Protection from loss of 'conversions'
2. Protection of reputation
3. Piece of mind

Assuming your service does indeed keep a client's site running as needed (and you really need to make sure you can actually deliver on this) you will be protecting the client in the 3 ways listed above.

Protection from loss of conversions: if their site breaks (or is hacked) and they're selling products that's a big problem. Even if they just want customers to be able to contact them that's a big problem. Keeping everything working is extremely valuable and WordPress really does need someone actively involved in this process.

Protection of reputation: Make sure they understand that if they are hacked it will damage their reputation. If customers cannot contact them or purchase it damages your reputation. If this bad experience is the customer's first experience with you they may never come back.

Piece of mind: This may sound un-important, but it's not. Knowing that someone (or some service) is always keeping your site up and running is huge. It's easier to sleep well at night when you know your core business functions are working.

It sounds like your service may go beyond clients for whom you have built a website. If this is the case there are going to be some extra difficulties in selling your services. I would probably need to know more to give you specific advice, but feel free to schedule a call with me if you want to discuss further. :)