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: 
The golden rule: The customer is always right - if the customer pays for it. If your manager comes to you and tells you that the customer is paying for a feature or a change, and tells you to do the work, then you do it. Otherwise you don’t. 

Find out who in the company can make a decision whether work will be done at all, and for what price. Then when you get a request, you say politely “I’m sorry, but this is something I cannot decide. Please contact so-and-so about it”.

PS Just because the customer is willing to pay doesn’t mean they get it. Someone quite high up needs to decide about the company’s strategy. Any request costs money, not just for the work done, but also for all the other work you *should* do instead.
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.