Is there a server management scheme with intentional partial uptime? I mean, a server that automatically sleeps at night? Or a server that wakes on every other hour (using hardware, not cron jobs) to do some cyclic task? Or two servers working in a collaborative manner -- one sleeps while the other works. If no, has implementing such a scheme any benefits? Such as, longer life expectancy or low power consumption?
I would call the general category power savings.
Automatically sleeping/hibernating the operating system is more common for desktop, where it may only be used for a third of the day.
Servers you might leave on to provide services or do maintenance tasks, but use various power saving modes. Although you can shut things down every night if that makes sense in your environment.
Deep idle states of processors cut down on power utilization, with the system still running.
Some hypervisor managers can automatically consolidate VMs and power off hosts for power savings. For example, VMware DPM, SCVMM power optimization, or XenServer Work Load Balancer. Virtualization power management: How to save money and the Earth
In the public cloud, automatic scaling spins up the correct amount of infrastructure for you. Or, you write a function to run as needed and not care about VMs. (Although, cloud bills are for the infrastructure, you don't see the power or hardware costs directly.)
For the every 2 hours task, it probably is simpler to run an appropriately sized, power saving server. Waking up to do the task is much faster with the system already booted. And idling only uses a few Watts of power.
Life expectancy is a tricky thing. If you have a disk array of spindles, keeping them spinning is probably better for them then spinning down and back up. Many components survive being online continuously for a few years until they obsolete.
IIRC both VMware and Citrix had such a power saving scheme primarily for their desktop virtualisation products (where the main workload will quite predictably almost always be on workdays between 8:00 en 18:00). You could manually or automatically plan to power down the majority of unused hypervisors (leaving some spare capacity) and then power up additional hypervisors when demand increases again.
With such servers running only 50 out of every 168 hours per week the power saving should add up.
In the world of cloud, where you pay for usage, scaling up and down your infrastructure and applications based on demand is standard as well.