Several days ago on a forum that revolves around systems administration, I had to read about the unfortunate situation where a sysadmin was overwhelmed by a problem related to his job that was ultimately out of his control, but was so taxing and so stressful that the person in question ended up committing suicide.
I'd like to address two things - both as a manager and as someone who has been working in this industry since the birth of ISPs in the mid-90s.
The first part is for managers and management in general. Owners, C-levels, managers, et al. - pay attention to your staffing needs. If you have a single support entity, for something IT related or anything else, and you require greater than 8x5 support, you are understaffed. Your reasonable expectation of work may be a 45-50 hour week; that's okay. It covers time needed for administrative functionality, meetings, etc. People require down-time, however, and if you are demanding 24x7 support from a sole employee, that person is working a 168 hour work week, and that's not just unreasonable - it's ridiculous.
What about 8x7 support then? You could go with 1.5 full-time employees, but you're going to have some waste. It's likely you're scheduling them in such a way that there's no overlap for their shifts, so one person can not easily pick up and carry things forward for another. You have coverage, but not a team. 12x5 support? same thing. You could fill it with 1.5 FTEs, but their cohesion will be minimal, and you'll have waste. How about 24x7? I'd suggest that if you truly need this, you'll probably need 5 FTEs - there are three 8-hour shifts each day to cover, and you have weekends to worry about where you could probably run 12 hour shifts and then have a bit of overlap and extra coverage for cohesion.
All of this serves the single purpose of not burning out your resources, not forcing them to be singly reliant in cases of emergency, and oh yeah - what about vacations? Americans are the worst about vacations, even more-so when it seems like if you leave, everything will fail. Possibly true in small shops, but there are other ways to supplement - if you can't have full time coverage, contract with a managed services provider that can handle your needs, it reduces your cost and allows the coverage need to be handled by the MSP, where the cost is shared by other clients. Or evaluate whether it makes sense to have a single FTE and supplement him or her with some other type of outsourced support.
In other words: don't let your business' success or failure hinge on a single technical resource if you are concerned that should that person no longer be available, your business will not run.
Part two is for the technical folks out there: your boss may not like what I'm going to put out there, but it's just a job. If you screw up, it's just a job. If you take down a critical server, VM, instance, or container and the business doesn't have a backup - you try and fix your mistake, but it's just a job. If your network is infected by ransomware and your boss has told you that backups aren't important - you help, but it's not your job... and hopefully your boss learns the lesson. If your data center is nuked from orbit (just to be sure), and there's no alternate and no DR plan... Polish your resume and start looking, because it was just a job.
If you can't go to sleep without getting paged 19 times overnight and you cannot or "are not allowed" to address the issues, your stress level is going up and you physical health is going down. If you work in a toxic environment where your boss screams at you for things you have no control over, your stress level is going up and your physical health is going down. If you have two weeks of vacation each year, but it doesn't roll over and your boss won't let you take it, your stress level is going up and your physical health is going down. There are more of these, but you get the point: if you are an emotional punching bag or a generic scapegoat - exit the situation. It is just a job and you are more than that.
Third, for both parties, it's important to set reasonable boundaries. As a manager, I have threatened to disable people's email to force them to disconnect. I don't want a bitter, burned out employee because that toxicity spreads. As an employee, protect your own time - most managers are looking out for the department or the team, and will put that above your personal wellbeing. "No" is a complete sentence.
If you're getting a salary for 40-50 hours a week, and your boss wants you to work the weekend, say "no." Lie if you have to - baby shower, bar mitzvah, wedding, funeral, any flying spaghetti monster holiday (personally, I like Friday), or just tell them you have to wash your hair. Especially if you are bald.
Working in the information or internet technology realm can be stressful for all parties - business is reliant on the technology to maintain productivity but putting all of that stress on a single resource, or even an understaffed team, can create additional problems when that stress causes the person or team to fail.
Finally, unless you are in military service or a first responder, very few jobs are worth trading your life for. It is better to quit and find a different job than to work in a situation that makes you constantly stressed out and miserable.