This is one of the biggest and common problems we encountered in the past where the server keeps entering down-time mode. Affecting some of our earliest client (thank god they are still with us 100%). It is more common to occur in shared hosting when some web hosting companies decided to be a bit greedy by stuffing many websites into a single server. When someone decided to use more of the “space”, the rest of the website sharing the same space will be affected. That is when you start sending “tickets” to the respective hosting company. By the time they respond to your ticket and check on your website, it is highly likely your website is already up, online. They will just tell you “your website is accessible now”, this cycle goes on forever, for a tech person it is called “infinite loop”. So yes, stability is the most important factor to consider when choosing the right web hosting service provider for your company.
It is true, most web hosting companies will not guarantee 100% up-time or no-down time. Usually they will tell you 99.9%.