Google's John Mueller said that moving to a new hosting company doesn't cause ranking declines. Of course he means if the new hosting company doesn't prevent GoogleBot from crawling your site. But in general, moving hosts doesn't have a negative impact on your rankings.
John said on Twitter "Moving hosting results in a temporary slow-down in crawling, but that catches up quickly & doesn't affect rankings." "Moving to a strong & fast CDN (like Cloudflare) makes sense for lots of sites," he added.
This was in response to a case study that showed a one-off where a specific webmaster moved to Cloudflare and their rankings dropped. John clearly is saying this is not true when he said "That post's just speculation."
That post's just speculation. Moving hosting results in a temporary slow-down in crawling, but that catches up quickly & doesn't affect rankings. Moving to a strong & fast CDN (like Cloudflare) makes sense for lots of sites.
— 🍌 John 🍌 (@JohnMu) December 9, 2018
So do not fear moving to a faster and more redundant hosting solution.
Forum discussion at Twitter.