I subscribed to a Virtual Private Server (VPS) which promises 99.99% of up time guarantee. But I often encounter down time, slow access time and I'm thinking about how to get them.Is there anyway/ service that allows me to prove that the web hosting provider isn't delivering the 99.99% up time guarantee? 
How to check on the 99.99% Up time Guarantee?
web hosting;shared hosting
The quick answer is that there are companies that monitor websites, pindom being the most well know. for a single site many offer free services. I use http://mon.itor.us theyb have a really nice user interface.If your website is unresponsive there are many other more likely causes than connectivity issues of your hosting provider. Ideally you should see if they will give you the address of another site on the same node, if both sites are down then you have good cause to blame the host. If only your site is unresponsive then you will need to do your own trouble shooting assuming the VPS is unmanaged.It's likely that the uptime guarantee refers to network connectivity, normally this is tested by looking for a ping response from your server. Even if you can prove the server was unreachable from multiple locations and that it was the entire node not just your VPS it probably wont be worth it. A typical SLA might offer days service credit per hours down time. Your efforts will be better spent migrating to a more reliable host than getting your current one.