Year later and no fainting on the bike. So I guess the problem is not too progressive.
I did have the problem other times though, back in 2008 and 2009. Probably five times total.
Once I had the bright idea of doing intervals up and down the canyon sides on East Broadway. Uphill, downhill, build up speed, uphill, downhill. A little of that and I was pooped. Rode toward home and got through the Broadway Railroad underpass when I couldn't continue. Lay down on the grass alongside the Medlock's building until able to ride home.
Another time on Canyon Drive, not riding hard but felt faint, so I lay on the grass at streamside, head on backpack, for 15 minutes.
Another time it was hot and I'd eaten a meal a bit earlier, I had to crash out under a skinny tree at what used to be Lubbock's public pool in Mackenzie Park.
More recently, think it was in 2010, I had to lie down at Broadway & Canyon Lakes Drive, right on the frisbee course. And again under the big elms at lakeside near the park entrance.
I'd bet that each time my bp was low. But don't see any uniform cause. Sometimes heat, sometimes hard riding, sometimes too soon after too big a meal. Sometimes after a sugary drink (possible hypoglycemia). Sometimes none of the above.