If You Feel Like The Other Person Keeps You Waiting, Don't Wait. Leave.

Let's say you are in a relationship. It does not matter in which kind of a relationship. It may be sex without commitment, or a serious intentions, some kind of relationship with a touch of love ...

In fact, any close contact with another person is a relationship. Even the one without obligations. The absence of mutual obligations is not a lack of respect, not a lack of tact, not a lack of attention to the needs of another person.

Every relationship is based on the fact that you are aware of your interests and recognize the interests of another.
If you care only about satisfying your needs, then you will become a fierce manipulator. If you completely neglect your interests, and you only worry about making the other person comfortable, then you will become a victim. All of these lead to dependent relationships. And “just sex” is the shortest version to them.

A healthy relationship suggests that the interests of both parties are satisfied.
If you feel the need for attention, but do not receive it, then either agree on acceptable conditions, or start looking for the person with whom you can satisfy your needs.
If you ignore the fact that your needs in a relationship are never being met, you become a dependent person. 

​If the other person keeps you waiting, if you are mentally attached to the one who must resolve your inner tension, then you must leave.

When you should leave. These are the situations:
... You write one message, second, third. And in response you get - silence. Or the answer to the fifth message, but then again - silence.
... you call, and he does not answer. Two hours later, too. A day later he responds. 
... you are waiting for a marriage proposal. He promised. But then he fell silent without explanation. Do not reach out, do not agree to his silence.
... you feel that he is not faithful. There are facts, but he avoids direct conversation. He twists the facts.

And there are many more situations when you feel a painful little trick has begun ...
Finish it. Perhaps if you have already become attached,  and it may hurt. But if you stay, then the pain will increase at times. If you need help or support, go to a specialist.
This does not mean that you need to write angry messages like: "Bastard, I'm leaving!" Decide for yourself what you need, what you want from the relationship. As a minimum, you need clarity and information. 

Of course, this is not about waiting for a soldier to comeback from a war or from an expedition. Here we are talking about the fact that a man who is accessible in every sense (there is a connection, the strength in the fingers to press the buttons on the phone) suddenly becomes inaccessible.
​He probably works hard and hard, and is fine if he has not answered within ten minutes and a couple of hours to your message. But if the message remains unanswered for days, not hours, then this is not very desirable.

You should not start coming up with excuses for him, looking for decent explanations for your silence. Each of us deep down knows that we will always find a few words for someone who is really dear to us.

Maybe a couple more nuances...
Suppose he is depressed, in such a real depression, which is a disease. None of your actions or inaction will change anything anyway. Depression has not speculative, but quite real signs: sleep loss, weight loss, food, anxiety, headaches, muscle aches, etc. You can only seek professional advice on how to approach the person, maybe insist on a visit. But the choice is always up to the person to decide if he wants communication.

Or a relationship has fallen apart. This is normal. All relationships have cycles and phases. You may not coincide in phases with your partner. He is moving away, you do not agree. He moves away, you begin to catch up, you fall out, but have to move away as well, though not willingly. This also looks like stretching an elastic band. He leaves and pulls you along. Then releases and stops. This is very unpleasant. But,  do not stop in life, stop in the race.
If you start waiting for someone or something, stop waiting. Return to your inner peace, to yourself. It always helps in normalizing relationships.