My boss says the servers need to be restarted at least weekly
I strongly disagree. Microsoft has made great strides since the good-ole [NT, anyone?] days with regard to stability and uptime. It’s a shame the consensus within IT support has not changed along with this.
How often does everyone restart their Windows servers?
Only when required — Either because of an OS/software update, a critical software failure which cannot be recovered via other methods, hardware upgrade/replacement or other activity that cannot happen without a restart.1
Is there an industry standard or recommendation?
I have never seen a standard recommendation, per se, but I could not agree with any recommendation [except from MS themselves] which would indicate a required reboot at a specific time interval “just-because”.
Is our IT department correct in saying that because we re-start that’s why we’re having hardware issues?
Restarting [and, more so, power cycling] is the most stressful period of hardware activity for a computer. You have most everything spinning up to 100% — disk and fans… …as well as significant fluctuations in component temperatures. Modern hardware is incredibly resilient, but that shouldn’t be a reason for just bouncing servers, on a whim, a few times a week.
1 Aside, I loathe when techs “just” reboot a Windows server in the case of a failed service, or the like. I understand the need to get the service running again, but a reboot should be the last step in trouble shooting a server. Identifying, and fixing[!], the root cause of failure should almost never result in “Meh, just reboot it….”