It's highly unlikely that moving web hosting would impact your rankings. However there are a few situations where your visibility could decrease if not accounted for:
During the move the website isn't available for a sustained period - crawlers won't be able to reach the content on the website causing your rankings to decreases over time.
If your server response time increases - make sure your new hosting is to the same performance standard, slow load times DO impact rankings.
HTTPS encryption - if your current website has a SSL certificate you will need to ensure this is updated/retained for your new server to retain the (small) existing ranking benefit.
