What plugins are you using on the sites? And what WP version are you on?
Read the "High load" entries relating to wp-cron getting called too often, in this forum;
http://wordpress.org/tags/wp-cron and see if you can pick out a fix
This thread also details cache calls being a bit of an issue for some people so you might wanna give that a try;
http://wordpress.org/support/topic/52452
Your hosting company are clearly a bunch of cocks, too often they advise upgrade rather than solve... I hate that