Do you have planned an emergency host especially before your site start eating more resources than all the rest and your current host can’t able to provide you with the needed service and most of the time keep messing with your site because that seems big for them to handle? Also do you classify your high demand or study the upcoming demand especially when your site traffic is growing somewhat without warning?
Possibly this is the right time to thrash a system and to get a host in advance from your list for emergency hosting who can set you up on a server on your own where you can thrash it. The support issues are more like to be an issue to the average kiddies host but a professional hosting company would get the occasional support call as their customers don’t have any issue, very occasionally there might be a genuine issue.
My point to start this post ; You should keep a host in advance in your list that has capability to help you to efficiently manage during such high availability requirements and or during some unexpected events so that in case you find serious lapses from your existing host side you can easily shift to another host from your preferred list. Also in case you unexpectedly expand an account you should be carefully managed to shift to another host preferably with your own server.