I've probably had 10+ events as Skipper on 737/757/767 aircraft regarding passengers reporting breathing difficulties. Fortunately I had great Cabin Crew and medical professionals present for all events and of those sick did not deteriorate further.
All did occur at cruise altitude, generally with cabin altitudes of around 8000'. One thing I did with all of these events was to descend to FL240 or slightly below to get the cabin altitude down to 3000' or lower. Maybe I got lucky or the portable oxygen had a bigger effect, but in all cases the reports from the cabin generally indicated that the sick passenger began to breath easier around the same time the cabin altitude stabilized at a lower altitude. Generally I didn't inform the cabin crew of the action until later.
This action of course depends on sufficient fuel available for the remainder of the flight. One descent required a climb back to the original cruise altitude to proceed to the destination or divert for fuel. Fortunately the passenger had no further difficulties.
Of course in most events, after arriving, most passengers were cleared as "OK" by the EMT's and were not going to be stopped from continuing onto their connecting flights.
