Short answer: no.
Long answer: yes but it's probably not worth it.
Most web hosting companies have Service Level Agreements where they say they will keep your stuff running something like 99.9% of the time.
That sounds pretty good right?
Well, 99.9% of the time is about 9 hours per year. A full working day per year.
Then, you need to look at what happens if you do get downtime. Generally, you are entitled to a refund as a percentage of what you pay per month.
Let's say it's a 30 day month. Which means 720 hours in that month. So if your site is down for 4 hours in total, that's 0.6% of the month. If you pay £10/month hosting (decent hosting is actually expensive and for some of my clients, that's insanely cheap) - then 0.6% entitles you to 6p in compensation. Even though your site was down for half a day.
Take Action: Find out what your hosting company's compensation policy is. Laugh at it and come up with a contingency plan, because your site will go down some time soon.