Vivacity 50cc cutting out when revved?

I have a Vivacity 50cc, and it has a tendency to lose power after about 20 mins riding when the throttle is open. It will tick over ok, but open the throttle only a little bit and it dies.

It could be a coincidence, but I find this problem can often start after going over a bump. It can also recover suddenly, but by no means all the time. It normally has to be left for a bit, then it seems to work again.

Any ideas what might be the problem?