Of course he has. 
Crappy musical?!? Lerner and Loewe? Cyd Charisse? Gene Kelly? It’s Almost Like Being In Love? C’mon - that’s a great show!
Black Hawk Down - a fine film, but hardly a classic.
Hmmm… maybe you’re right. 
There’s a lack of both physical and emotional intimacy and he’s not willing to put forth any effort to improve the situation. That, alone, is reason enough to stop seeing each other.
Whether the reason for the lack of intimacy is his sexual orientation or something else is beside the point - he’s expressed his feelings on the issue and you have to deal with that on your own.
“If there is a simple explanation for most of our problems, it would relieve some of the bitterness I feel about the way things have turned out.” Sorry that you feel bitter, but you’re only prolonging the bitterness by trying to figure it out - time to move on.
INAS (I’m not a shrink) but I would think if he does have some sort of sexual dysfunction, asking him if he’s gay might make matters worse. That is, if he isn’t gay.
Think about it for a second. He’s having some weird sexual issue, perhaps left over from a weird past relationship or maybe childhood abuse. Then his girlfriend starts asking him if he’s gay because he shows no real sexual interest in her. Man, that would kind of suck if you ask me.
Some people just aren’t very sexual. Or, just maybe, he’s got a fetish you don’t know about (of the non-penis kink)
What I would do is introduce porn into the picture. Pick up a couple of different titles aimed at different bents. Big tits, blowjobs, leather, lesbian, anal, femdom. See what gets him going.
If you really wonder if he might be gay, pick up a bisexual movie where the guys do the girls and the guys. If that gets him going then you might be on to something. But the last thing I would do is come right out and say “are you gay?”
I second the hypothesis that he’s just not that into you anymore. I know a couple going through the same thing right now (they’re getting divorced). The’ve been together for years but their lives have been moving in different directions. She has a very high profile PR job with her company where she travels all the time while he’s become very “Joe Sixpack” and has had some career issues of late. I imagine that a combination of resentment, jealousy and agitation can and has built up over the years to the point where they can barely stand to be in the same room, much less have sex.
While it is possible that he is gay, more likely that there are other problems in the relationship. Contrary to popular belief, we guys can say no to sex.
Now Bricker I’m pretty sure might be gay.