Hi Troy, thanks for answering.

There's always a little bit of a pH shift when I do a water change but I don't think it's that causing the problem because the other fish aren't affected at all and the afflicted fellow was panting before the water change. He hasn't been right for a couple of days.
It's like he just can't get enough air - he's constantly gasping / panting. I've increased the aeration in the tank but it hasn't made any difference. I suspect gill trouble - flukes, or maybe other parasites. I was thinking about trying salt at 3 tsps per gallon (added in stages of 1 tsp per gallon every 12 hours).... can neons tolerate salt?
EDIT: I forgot to mention he has also stopped eating today. He showed a bit of interest in the food when I put it in, but just drifted away again rather than eating any. Would it be possible for something to get stuck in a neon's mouth like goldfish get gravel stuck occasionally?