I stated that the organization would be in trouble of losing their
501(c)(3) status, not their nonprofit status altogether.  What would
happen is the organization would be classified as a charitable foundation.
 This means that not only would they have to pay income tax on ALL income,
related or not, but anyone who would like to give a donation would not be
able to claim a tax deduction for that donation.

Many museums are in such dire financial problems because they don't manage
themselves as a business.  Just because you are a nonprofit does not mean
you are not a professionally organized company, and it also does not mean
that you can't make money.  As in any business, you should carefully
examine any income generating activites, and consider what effect they
would have on the health of the overall company.  Too many museums are
tempted by the opportunity to earn a quick buck, without asking themselves
why they are getting into such activities, forcing themselves to be
experts in fields that they are not designed to be in (e.g. travel).