If you survive more than ten years of education, and at least eight of those in graduate school, you probably eat stress for breakfast. On the job stress in Egyptology is much the same as it was in grad school: 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. You'll deal with stress from colleagues and also from people you have to work with outside the field. This will come from people including government officials in Egypt and whatever country you're employed in, to university directors, to family that has no idea why you can't go on vacation because next month is the Old Egyptian symposium you're chairing and your major presentation on the second tense plural isn't quite finished.
Academics are generally petty individuals, which can make them stressful to deal with. The effect of thousands of scholars in a room that only has seats for hundreds (and thousands more trying to get in that door at any time) magnifies the pettiness, because the competition is so high. The hassle with dealing with concessions and governments if you are an archaeologist can be just hassle, but when your funding, and thus your livelihood and potentially your future in the field, are hung up on whether or not some person behind a desk signs the forms in triplicate, and that person operates according to Egyptian time ("it gets done maybe"), it can be a tremendously stressful situation.