I had same whereby it would stall after around 15 mins and then not start again. Turned out to be the air control valve. Like this:
http://www.ebay.co.uk/itm/HONDA-BEAT...4AAOSwGYVW~aos

If it sticks then the engine it starved of enough air tho start (when hot), guess it's a known fault if they're available on like on eBay.