When going in vacation for an extended period of time, meaning 1 or 2 weeks, would you consider leaving your bunny to a pet-boarding place? Knowing that rabbits are vulnerable to stress, would it be safe for them?
Most pet boarding places do not have sufficient experience to board rabbits. Many will not take them, and some that will do not know how to care for them.
You are correct that stress is potentially fatal see the related question Can a rabbit be scared to death?
In my area there is a local rabbit rescue (http://www.rabbitwranglers.org/) that also provides provides boarding services. In the case of this organization, there is no facility, everybunny is in someones house. You take your rabbit that is being boarded to the house of one the volunteers, they care for it while you are gone, watching for diet changes which is one of the primary concerns often overlooked by the inexperienced. In general providing a safe home environment for your bunny. You may be able to find similar services in your area.
The other two options I would consider:
Have a neighbor come to your house daily, to check the food, water, hay and empty the litter box.
Take your bunny to friend or family member. A cool place in garage or basement with daily care is going to be much less stressful then a boarding house with rotating staff.
Lastly take you bunny with you. We take our rabbits camping on short and long trips, I have a brief answer on traveling with rabbits here