I'd say occasionally. You know. May sees a Pikachu, or a Ash like hat (TDF's sig says it all). Ash sees.... a bandanna... or is in a contest.
You know. They think of each other
You're born, you take s-. You get out in the world, you take more s-. You climb a little higher, you take less s-. Till one day you're up in the rarefied atmosphere and you've forgotten what s- even looks like.
Yeah, I'm more willing to bet that it's just every so often. Partly because Ash's mindset is primarily on his gym battles and such. Although I wouldn't be surprised if May thinks of him more often than he thinks of her, and a lot to do with that would be the fact that she is traveling by herself and there's a higher probability that she'd get lonely sometimes, and then therefore reminisce about her adventures with him.
^ Well, maybe if they were actually a couple or something...possibly. But considering the fact that they are at this point still just friends, I don't really picture them thinking about each other all that much. I mean, sometimes, sure, but several times a day...eh, only maybe if, like you said, it was a day where nothing else much was going on. Then I guess it could happen.