Practically all host providers will assure you they constantly monitor their networks and websites. While I won’t accuse them of lying exactly, I will say that my experience is that I often catch problems either (1) they were unaware of, or (2) before they were aware of them. Hopefully your webhost will offer some sort of network status site or hotline to consult before opening a trouble ticket. Before that however, you need to know when your site goes down. Thankfully, there are numerous monitoring services you can use. Two that I have used that are free of charge for basic accounts are SiteUptime, and InternetSeer.
One point worth mentioning is that sometimes you may think your site is offline when, in fact, it is not. There could be several reasons for this. So, before calling your hosting company to complain, check out my section on troubleshooting hosting problems.