When, in a relationship, do you stop looking at others and just focus on the person you are presently dating?

Recently, that has been a hard call for me.  While I enjoy the person that I am presently dating, she always seems distant and only moderately interested in me.  So, I never know if she is going to dump me.  And because of this, I am reluctant to close down my dating web sites.  But, at some point in time, I am going to have to take a chance and commit.