G-Unit has brought up a really good point when she stated that Ray does want to consumate his relationshp with Neela without her first giving him her heart. He doesn't want to be just another guy she sleeps with because that's all she can seem to share of her self with a man.
Ray had been a player in the past where getting a woman into bed was more important than winning her heart. Falling in love with Neela changed all that but it wasn't until he hit rock bottom that night of Luby's wedding and got into the accident that would change his life forever, did he finally realized that he wanted so much more from a relationship. He had been able to sleep with a woman just for the physical pleasure of it and not have to engage his heart into the mix. Neela was the one woman he couldn't just have a meaningless fling with and that is because she was able to penetrate his rough exterior and reach his heart.
Just as G-Unit said, Ray doesn't want to go back to being a pathetic pupply pining after a woman he feels does not love him back. He wants to be loved and finally feels as if he is worthy of being loved so if that means trying to move on by dating other women in hopes of finding that love and as a result giving up on Neela having a change of heart, then I don't begrudge him that.
I do believe that deep down Neela is in love with Ray and has been for some time but has allowed her fears, guilt, and insecurities keep her from telling him. I only hope that when she finds out about Ray meeting a woman at the gym that it causes a major wake-up call that if she honestly wants to be with Ray she can't continue to waste time rather than her taking the coward's way out and just giving up entirely.
When thinking about all the possible scenarios that would be the final catalyst to getting Neela to go and fight for Ray, none of them involved an emotional phone call or email/IM between Ray and Neela but I think it might be an avenue worth exploring.
I'm not sure exactly how the conversation would be instigated but in it Neela can ask Ray why he really left her apartment that night instead of accepting her invitation to stay. Ray could then confront her with his belief that there was more going on between Brenner and her than just a working relationship and he didn't want to play the third wheel like he had before with Gates. Basically Ray needs to say to Neela that he doesn't want to be just another guy she sleeps with and that he wants more than her body; he wants her heart but if she is not willing or able to give that to him; then they will never be anything more than friends. By saying this to her he is laying it on the line and putting the ball in Neela's court so to speak. It would then be up to her to decide just what and who it is she wants. It will give her some serious food for thought.