Thanks for your response Steve,
In my case, this would be one public institution, one private (but open to the public). Both requests were for on-site listening of audio, requiring 1-2 hours of transfer work in advance. In both cases I was open to paying duplication fees but both requests were denied for administrative reasons regardless. The first because the collection was not processed, which seems like a fair condition except that this particular collection had been with the institution, unprocessed, since at least the 1980s. In the second, the entire format (commercial brown wax cylinders) has been categorically closed to research because administrators have decided that they are too fragile to digitize. I don't think this is the consensus of other institutions with similar holdings, but that's where we're at.
I've had a few responses off-list that I found interesting and want to share. I should say, to start, that I meant the employee would be researching for their own interest, not on behalf of a third party. Reasons to deny a request or close a collection have included donor restrictions or privacy, risk of damage or theft, or unreasonable extent of a request. Beside those, people have said that archives that serve the public by charge are obligated to provide access, and whether or not the requester is staff shouldn't matter. One person did say that some archives prefer to hire staff who don't have independent research interests. Nobody has said that their institutions have a formal appeal process, but two said they think it is appropriate to appeal a decision by raising the issue with higher-level administrators.
The one to two hour limit for remote requests is interesting. I would be interested to know if other archives handle these similarly. I have also had mixed success with this kind of query but for now I'm mostly interested in policies or practices related to on-site research. Anyone else care to weigh in?