Stress is not an outside force. Stress is within you and can only be allowed by you. If you control your mind and create internal peace within your environment, you can be stress-free regardless of what is going on around you.
Some people are stressed when they have nothing more to worry about than whether their socks match. On the other hand, some people are calm and relaxed while people around them are panicking and screaming at them.
It all depends on the person.
So, now that I'm done philosophizing, the pressures that come with being an automation specialist can be pretty high, but depending on where you are in your career and personal growth, can vary greatly.
For example, as others have already stated, if you're early in your career and find yourself in the field doing start-up on systems with which you are less-than-thoroughly knowledgeable, the pressure can be very high. If, however, you have learned strong troubleshooting skills, proper tools, and have in-depth knowledge of the system on which you are working, the pressure can be significantly less.
Later in your career, when you've reached a more senior level, the pressure can mount again when you become responsible for core design decisions or begin managing others. Again, as you gain experience with those and develop with your people, the pressure can often lower.
Finally, as you get really, really old, you get grumpy and can close the door to your office. People leave you alone. Sometimes they will slide papers under the door and, sometimes, not. This is your goal, the ultimate target. No pressure and no stress unless, of course, your socks don’t match.