It is very important; security, backup, maintenance etc...
The problem is there are two kinds of customers, cheap and cautious. Cheap only wants to pay $12 a month.. and does not understand or want to understand that not having maintenance is a bad idea. The cautious ones pay anywhere from $50 to $500 for a managed WordPress web hoster for their site. Why would they trust you? So what you are saying is that you want to educate the first group to understand they need help or get the second group to trust you more. Both are very hard sales... What I do with both these groups is sell them management included in the price of the full package. I don't know if your doing something else here. Another interesting Idea that I had, but don't have time, if your really good with fixing WP, let them break it and then charge them to fix it... Might be an easier sell.

This can be as simple as putting a message on your own blog.

Promoting it to your audience and potential clients is what I suspect you need some support with from reading between the lines of your question.

Firstly I would start with the top 10 questions your existing clients ask you.
This will form the basis of your own content inbound marketing - it will also start to set you as the authority.

Video case studies will work extremely well before & after style

Armed with this new information you can promote this to you network - email - facebook - twitter - linkedin - etc.

You might also want to use paid solutions which you can start for a few dollars a day to generate exposure for what you do.

What markets...? A better question might be who do you want to work with..? What types of businesses interest you?

When you have that info you can literally drop your awesome content in front of them with the type of advertising and targeting that is available to everyone.

Good luck

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. :)