Afraid of being dumped? Afraid of having to break up with them? Whichever, the following may contain help and influence.
If you're afraid of being dumped, there could be two things going on here. Either, you are noticing several little things that seem like the other person is becoming un-interested in you, and you think they're going to dump you, or, you are noticing differences between you two and you want to break it off. So, to start off, I will cover if you are thinking they want to break.
Noticing little things that bother you? Do they make you think they are not interested? Yet again, two things could be going on here; either 1: you are right, and they are trying to make it clear that they are losing interest and they are afraid of breaking it off, or 2: you are paranoid and creating problems for yourself. First of all, if they are making it clear they are becoming un-interested; they will have given quite decissive hints to this. Either they are constantly avoiding you, telling you to NOT call, etc. Or, you are mis-interpretting what they say through paranoia and you are creating your own tangent in your mind that will cause further problems. Put simpler, you could be counting very little things and blowing them out of proportion and thusforth creating alot of tension for yourself and your other. If this is the case, you most likely will deny it and are not aware of it. Although, if you have noticed that alot of your suspiscions are incorrect, or, when you confront your other about these problems and they become profoundly agitated by your paranoia, it is most likely that you are feeling insecure about your relationship and you are creating problems for the both of you. Reasons why you might do this are many, most commonly, it is because there has not been much experience in relationships, and thus, you may become paranoid due to in-experience; which is common, so don't beat yourself up over it; it's normal, although, it doesn't help your relationship problem. If you know the case is that you are creating your own problems (which is honestly more common than the other scenario) then, the best suggestion is to try and relax, realise that you are the instigator for your problems and tension. If you cannot comprehend this and deny that you are the problem in the relationship, then there isn't much hope of a future in your relationship, for it shows that you mis-trust your other (or they might get that impression) and that will cause many problems.
If paranoia isn't your scenario, and they are being decissive about not wanting to be with you, yet, they do not confront you about it and speak about it, it is then because they feel insecure and worried about hurting your feelings. Commonly, this is with the females. This is a hard thing to comply with, for the yielding of confrontation to the problem will cause many more problems; it is like a rolling snowball. This also means though, that they know that feelings are not mutual although they want to still associate with you. In this case, the problem will be recieving the news about them not wanting to be with you (although it may already be quite clear). The only way to deal with this is to know that they still respect you (at least they didn't dump your ass, stand you up, etc.) so remember to give repsect back. No one expects, and you are in no way obliged to not be hurt by their feelings and their motivations towards your relationship, so take your time and heal. Hopefully, in due time, you two can be on better terms and still be friends (sadly, although, that is not common..).
If you are confused about your feelings towards this other person, this is very common and a hardship all the time. There is nothing you can do to assure yourself of your feelings about this other person, other than being with them longer and learning more about them. The more time you spend with them the more you will learn of how you two feel for one another. This is a common situation which many of us deal almost all the time; it is a common human emotion to be unsure of your feelings and wether or not you should act on them. If you are afraid of your feelings, however, this may be a different scenario, which I'll cover in a little bit. Do not let your feelings bother you, for they are your feelings and how you feel. Eventually your true feelings will come to you, and you will know how you feel towards things. Remember that uncovering feelings takes alot of work, but you will eventually get there.
If any of this bothers you, or you are angry at me, etc. Please remember that I am trying to bring your true feelings to your open eyes, and any advice is just that; advice. You do not have to read or acknowledge any of this. You chose to come here, and if you did, I assume that you are seeking help, or you are bored. Either way, I apologise if I have offended you in anyway.