The question is not really when you should walk away, but IF you should at all. The answer to that is no, you should not.
If that is all there was to a relationship, the world would be in a sad state of affairs.
But, for the sake of this article, let us answer the title question in depth.
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Can you survive a sexless partnership?

That depends on the individuals involved. Some people are very happy even with a lack of intimacy. Other folks find it extremely difficult.
If the latter applies to you, it is probably best to terminate the relationship. Otherwise, you may wind up cheating. That is not good for either of you.
It can depend on WHEN the lack of intimacy began
If you were enjoying a nice and passionate romance and suddenly the intimacy ends, it can leave you with many unanswered questions.
For example, is the other person cheating? Is there something wrong with you? Do they have a serious medical problem?
Answers to these questions can help you decide whether to stick it out or not.
Should I try an honest conversation first?

Absolutely YES. Especially if you did have romantic interludes and now you do not. A conversation with your spouse is definitely in order.
You really need to know why he or she no longer wants to have sexual relations with you. If they refuse to discuss it, perhaps it is time to exit.
Can a counselor help?
Possibly yes. Do keep in mind that your partner’s counselor would not be permitted to talk to you about what he or she has to say.
The idea is to get to a point where your significant other can talk to you about it. If your mate will not do that, it is probably best to end the relationship.
Are you wrong for wanting to leave them?

This is not necessarily a right or wrong decision. The answer to this question has to do with what you want out of the relationship.
If you truly love this person, it may be fine to go without sex. On the other hand, if you are miserable, living a lie is no good either.
Nobody can force another person to submit to their will. An issue like a lack of sex can be a major one.
Is it possible for your mate to have a great reason for this?
Yes, it is. The reason could be a medical one, a mental one, or an emotional one. Maybe their job is stressful and exhausting.
At the end of a long day, he or she is just too tired to perform. Perhaps your mate feels inadequate in the bedroom.
These are also reasons to seek professional counseling.
Have you become unattractive to them?

Sometimes when you and your spouse stop having sexual relations it is because one of you no longer finds the other attractive.
No amount of counseling can help with this. The only solution is to go your separate ways.
Is your spouse seeing someone else?
This is a distinct possibility. There are ways to go about proving this. If the answer is yes, then walking away from them is likely your best option.
If they are not, your relationship can probably be spared.
What if we’re not married yet and intercourse has stopped?

If this is the case, then getting married will not end the troubles. You two should probably not consider marriage at this point unless there is something physical that prevents one of you from having sex.
If you really care about each other and sex is important to you, do something positive about it. Or else, split up and find a new partner.
Can time resolve the lack of sex?
Not by itself, no. The matter will only fester and make both of you miserable. The key to solving this problem is getting to the root cause and fixing it.
If solutions cannot be found, no amount of time will change that. Some serious discussions between yourself and him or her are in order.
Is a lack of intimacy only on the part of the man?

No, there are just as many women who stop wanting sexual encounters with their partners. It is not a gender-specific thing.
The issue can also occur in same-sex relationships. It is not exclusive to heterosexual couples. Again, heart-to-heart talks may be able to resolve these problems.
Does a person’s age influcence their sex life?
Sometimes, yes. As people age, two things happen. First, they lose their desire for intercourse. Then, they lose the physical ability to have it.
Your spouse might feel ashamed of this. If you really love him or her, you two will come to a peaceful resolution.
That resolution can go either way as far as having sex goes.
Is it considered healthy to stay in a sexless relationship?

The answer to this question also depends on what both of you want from your relationship.
If you are truly in love with each other and a lack of sex is your only problem, then it is healthy to stay. There are other ways to demonstrate your love.
Maybe the children are to blame
This is not meant to be cruel towards children, just truthful. The presence of children in the home can cause a lot of sexual problems.
This is especially true if they are particularly demanding. While you and your spouse are spending time taking care of the kids, your personal relationship can suffer.
This includes your sex life.
Perhaps you have been too critical of them

If you have been critical of your mate after sexual relations, this can be detrimental to him or her.
It can cause a lack of self-confidence and make them not want to try anymore. In fact, criticism of your partner’s performance can be traumatic to them. Try to avoid this.
Outside stresses can be factors
We already talked about your jobs being a source of stress. Maybe there are problems in your immediate or extended families.
Perhaps your friends are contributing to your stress load. When one or both of you are stressed out, performance in the bedroom can suffer.
See if you can eliminate at least some of your stress.
Is there a pregnancy involved?

Pregnancy can also result in a lack of sex. It can be difficult to perform around the huge stomach she now has.
Maybe the man of the couple is afraid of causing harm to the unborn baby. Perhaps he finds you unattractive during your pregnancy.
If this is the reason for the lack of intimacy, see if it goes away after the baby is born.
Has one of you betrayed the other?
Even if it is yet undetected between the two individuals, a betrayal can lead to a lack of sex. The person committing the act of betrayal might be feeling guilty about it.
The result can be the inability to perform in the bedroom. In such a case, the betrayal itself is a reason to end a marriage.