There are two types of rejections soft and hard.
Soft Rejection: Soft rejection is the most common type of rejection. Usually the rejection is very short and goes along the lines of "I'm not interested" or "I don't need your product". The reason why this is a soft rejection is because in fact this is an objection mascaraing as a rejection. Handling this rejection would be the same as handling an objection.
For the follow up you have to assume that you have done a perfect job explaining a product or service. Therefore, it is very surprising that a prospect would not want your product. The most logical response would be to ask a customer why they do not want the product and what you can do in the future to improve: "I'm sorry Ron that this was not a right solution for you. I am little surprised, however, because this solution is in such a high demand. What feature you did not like in particular? I am only asking because I want to improve our product in the future". With this approach you are putting a prospect in an awkward position because it would be rude not to help you out. If they answer your question, you just got another objection which you can now handle because a prospect revealed a true reason why they are not going forward with your product.
If a rejection comes via email this is actually a buy sign. Most customers do not respond to cold emails. However, if a prospect did it indicates two things:
They are engaging with you
They are evaluating your product
You must respond to these emails instantly. Because a prospect is open to communication write out a long email apologizing that they did not think the product was useful and then go in details of the benefits of your product. Apologize that you have not been clear before and suggest a time for a meeting for you to have an opportunity to explain the benefits of your product better.
Hard Rejection: You will know this is a hard rejection by tone. Usually someone asks you not to approach them again or they do not see the value in your product. This is a hard rejection because there is no way of handling it. However, just because you did not sell anything, does not mean that the relationship has to end (even if a prospect insists they never want to see you again).
People like to be in control and you want to put your prospect in control so that they are not fearful of you. One way of doing that is asking their permission: "Ron, I understand you do not see value in my product but do you mind if I give you a call 2-3 times per year, just to let you know about exciting features that are being added to our product line?". If the answer is Yes then you have an invitation to call few times per year and continue to build relationship; become someone they know. If the answer is No, you can still do call them but wait a year. Your call after a year would go something like: "Hi Ron, its Tom from XYZ cleaning, I called you last year but a lot of time has passed by and I just wanted to tell you about our new service...". Usually you are able to restart relationship because you did what the prospect asked for: did not contact them for a long time.