The IP address on which your website is hosted does make a difference in the search engine rankings of your website. However, it is said that the loading speed of your website and the time for which the website remains offline affects the search engine rankings of your website as the algorithm of search engines can determine the time for which your website was offline and the time it takes to load.
Also, if your website is updated regularly, some of the search engine spiders remain on your website to make sure that the updated content is indexed in the search engine soon. Hence, if your website remains down for some time, the search engine spiders get this information which can definitely affect the search engine rankings of your website