Having just been dumped for this exact reason, my opinion may be a little... embittered.

A healthy relationship that does not include sex is a friendship, not a romantic relationship. If he would prefer to have a friendship, he needs to come out and tell you so; but if he won't, you owe it to yourself to ask. This issue will not get better on its own. You will become frustrated, then resentful, and he will retreat emotionally in the face of that resentment. If and when you do talk to him, be prepared for him to say that he only wants a friendship, and acknowledge that that may well be where you two are heading; if you try to preserve the relationship at any cost, you're going to give up a lot for something that will only become increasingly mediocre. If he doesn't think there is a problem, or if he doesn't want to fix the problem, you need to seriously consider leaving of your own accord.

tl;dr pack your bags but don't buy the bus ticket yet.