Vespa t5 cutting out

hi there all, my 98 t5 is starting to be a bit of a pain.
its stats first kick in the morning rain or shine , but u go down the road about 1/4 mile and it then cuts out, then there is no spark ,if i leave it for about 3/5 mins it starts and runs all day , changed the spark plug leads and cdi , still no good, was thinking of the pick up .any help thanks

petrol is going to carb,
i tryed somthing else . i had it running outside house on stand till it cut out .did not take keys out or move the scoot, tryed spark plug in ht and no spark , so i left it and went and did some things for 5 or so mins, put spark plug in ht and it [sparked ,?it seams like its the same amount of time each time it does it.
thanks dav [:rolleyes:]

check your stator plate the coils and black box are allright .also check all the daft things first carb broken wires