It's quite possible that you're not being given a large allocation of CPU resources and, because Moodle is a fairly resource-intensive application, simultaneous accesses are going over your limit. It's understandable why the host would do this (to be nice to other users) but you should be able to stop this from happening by limiting the number of simultaneous accesses by users. You can talk to you hosting company about asking them to put a load-limiter on your script's CPU time, or limiting the number of concurrent connections to your site.
Alternatively it could be because of your cron script [this is more likely]. Try logging in to your ISP using SSH or Telnet and running your cron script (from the Moodle root directory you'd type "php admin/cron.php") and see what it outputs, and whether it terminates in a reasonable amount of time [ie within 30secs - 3 minutes or so]. With 10 students it shouldn't have much to do. Maybe your hosting company is limiting how long your cron script is allowed to run, and limiting your access for a few minutes afterwards if it detects the cron script still running. This is again something to talk to them about.
Hope that helps!