How much do you charge for hosting mobile sites?

Hosting a mobile website can fluctuate in price and is entirely upto you.
Anywhere from $200-500 depending on difficulty and client.
I have heard of people that have also done elaborate 7-8 pages and charging $600+

With around 25% of people using only mobile for internet access in the U.S its a smart idea.
If any problems there are also alternatives such as sites like dudamobile.com

I'm not sure how you will explain to your client that you wanna charge them other hosting fees than the ones that they already pay, unless you sell them a package, administrated entirely by you along with mobile seo, qr codes, sms marketing ... and charge a bigger monthly fee for all these services.
Think about the long term business that your future clients can bring in terms of design, redesign, seo, offline marketing, referrals etc ... I wouldn't charge for hosting since it can be hosted on their existing account.But if you want to be in total control include it in a marketing package.
Hope it helps.

What is the benefit to the customer to pay another hosting fee for their mobile site alone?

Of you can't answer that, move on.

If you were to charge them upfront hosting on a monthly basis, going low could be a good idea since you can make a ton on the frontend, but going high is not too big of a deal. Just know when it can be too big of an investment for the business.

I mainly sell mobile sites, and they can be sold very easily if you market them well and show how valuable they are. The problem for most people is that they charge too high both upfront and on the hosting that they lose the client.

I would at most charge $150 per month, but I usually go down to around $75 or $99 per month. Of course, I don't do much maintenance on them, just a few small tweaks here and there. However, if you are seriously providing work for them each month, you could charge higher, provided that you are going to deliver them a lot of monthly changes and updates.

I am not afraid to go low because the creation I charge could go anywhere from $199 to $599 depending on the size of the site and what it is they mainly want from it.