need some feedback, relationship in trouble?

So, I have a problem. I have been in a relationship for a little over 4 years with an beautiful woman. In the beginning it was all about us everything  we did, we did it together. Everywhere we went, we went together. I gave up a lot to be with her (moved, came out yikes!)  We were never big at communicating but I always figured that it would come in time. Over the years it has gotten worse, I like to argue and she hates it. I like heated discussions and conflicting opinions. She hates to even talk about controversial topics because we end up in an argument (is that so bad, at least we’re talking right?). I don’t get mad when we are in these discussions but she gets very irritated and won’t talk to me for a couple of hours. I try to explain to her that I like to hear what she is passionate about and even more I like to have conversations that don’t revolve around her work or the people she works with. It is seriously all she thinks about.  I have always thought that strong opinions backed up by accurate facts are hot, even if I don’t necessarily agree with them.

Lately she is always at work, and I mean always. She works every weekend and I only spend about three hours with her on any given day. She isn’t cheating, I’ve considered it and decided that she wouldn’t do that to me. About 5 months ago I decided that I may be a big reason our relationship has declined. In turn I have taken steps to correct the things that I hoped were the problem. I have been working out everyday (on my lunch break so that it doesn’t take away from our time together) trying to make myself more desirable. I have tried to make sure that the house is always clean and make sure the laundry doesn’t pile up. I try to set up activities for us to do on Sundays (her only day off) so that we are spending time together without a TV. Nothing I do has made anything any better. I even let her have a 45 minute nap when she gets home from work because she is so tired. We rarely make love anymore and if we do it is when I initiate it and most times not even then. It probably sounds like she is cheating, I can assure you she isn’t. Unless it is an emotional affair. I hope not. I love her and I know that she loves me but I’m  unsure if it is the kind of love you can base a long term relationship on.

Ladies please let me know if you think that this relationship is worth the effort. I don’t really know why I am asking, I won’t leave her unless she does something unforgivable. I guess I just miss having feedback.