Some failures I experienced and had to monitor/detect myself were: overheating (they replaced thermal paste when I told them I saw strange readings from the CPU stats), raid disk failure or ssd high burn (ie. partial failure, server still running, they replaced the failed disks after I told them).
Most of the time the issues have been resolved within 1-4 hours on low-cost Kimsufi and SoYouStart offers, even on weekends and nights. Often when the server is running they can require a shutdown.
I'm quite happy with this as I am highly technical in those subjects and like to look under the hood, but with dedicated servers you really have to do some more maintenance/monitoring/planning yourself.