If you survive more than ten years of higher education, then you probably eat stress for breakfast. On the job stress in Egyptology is fairly low key, especially if you're working on a dig.
The job itself is where the pressure is at. You'll have to deal with constant job insecurity, whether or not you'll have a job or get to keep a job in a bad economy, whether or not you can find funding for your next project or excavation, etc. It's like going to Las Vegas every time your funding runs out.
Then there are the lovely people you have to work with outside the field. We're talking about the government officials of Egypt, the U.S., and any country in between that assists in your work. The hassle of dealing with concessions and governments is not great especially when your livelihood is hung up on whether or not some person behind a desk signs the forms in triplicate.
You'll also deal with stress from colleagues. Don't forget that this is the world of academics: the competition is high and the competitors are intelligent and often slightly petty.