You cannot rely on wp-cron for consistent results so you have to look to the server level. Most enterprise-level Wordpress installations need some sort of consistent automation. This is how I automate WordPress in this type of situation.
You will need to add a crontab to the server itself. If you're running Linux, you can use
crontab -e to get to the edit screen.
Then add a simple curl command to hit your site on a regular basis:
0 * * * * curl http://yoursite.com/ >/dev/null 2>&1
This command will run once per hour. The bits at the end send the output to null and removes the email functionality every time the cron runs.
I use this on my sites to get around wp-cron's fickle 'scheduling'. If you're not positive about creating a crontab schedule, check out this handy tool for generating a crontab command. http://www.robertplank.com/cron/
If you're on a shared host, hopefully you have cPanel which if enabled, will give you a GUI to add a cron job. If for some reason you can't add a crontab, I would consider finding a host that gives you shell access and allows you the flexibility you need.
I've never used a cron hosting service, but you could check it out if your host won't let you add a crontab. http://www.easycron.com/ is an example of a cron host. (Again, I don't know the reliability of these services)
Hope this helps you!