Question: We are a small team of developers making and maintaining a software product with a high number of users. 

We are also in direct contact with users who ask us many requests about the product. 

We don't have access to business information (what kind of deal a specific user has with the company that employs us). 

We don't have enough resources to address all the user requests, and will have to refuse some of them. We treat in priority the requests that seem easier to comply with ; or that could benefit most users. 

How can we gracefully notify those users who made requests that we will not be able to process?  

How to tell them that what they asked for is not possible ; while avoiding frustrating them?

Answer: 
> 
> We don't have access to business information (what kind of deal a
>  specific user has with the company that employs us).
> 
> 
> 

This is the key thing. Unless you know the contractual details of a customer you can't make a decision as to how to reposed to a customers request.

The obvious thing is boot the request further up your managerial tree until it hits someone who can make that decision for you. 

In fact all change requests should be filtered through someone who is aware of the contractual requirements before you even start to work on them. As while you may think that an item seems reasonable, it may be totally out of the scope of what your customer has paid for, and by working on it you are effectively giving away free work.
Get together with your sales people/whoever manages the business side of the contracts for which you do the development. You have information they need, and they have information you need.

You need to know what you *should* do for the clients. The sales folks need to know what you *could* do for the clients, and how hard (read: expensive in salary hours) it would be.

You don't want to sever all contact with the customers. It's good if developers have a clear idea of what the customers actually want to do with the software. But you do need to get the sales people involved more. Handling your problem, is part of their job.