Rails said..
Riding downwind is actually one of the hardest skills to learn because you have to actively keep wind in your kite
Getting pulled downwind is easy
Sounds like you are pointing too much downwind in light winds
Without appropriate resistance the kite will stall
Need much more heelside edge to build this resistance and fill your sail
Exactly my thought
''working the kite'' could be a good idea in lighter winds but only once you build up apparent wind i.e. edging against the kite with speed.
It doesn't sound like you are at this stage yet in light winds, so to create apparent wind you need solid speed during the water start (hard power stroke), obviously harder to do this in lighter winds. You then must begin to edge the board
progressively just before your speed start to decrease (otherwise you sink).
Edge too much or too soon and it doesn't work. Edge too late or not enough and it doesn't work either.
Pull the bar in too much and it chokes your kite, Push the bar out too far and you don't have enough.
Getting a bigger kite or bigger board are both good ideas as well but contrary to popular belief you are not wasting your time in lighter winds. As long as you got a certain minimum of wind and you persist with this exercise, you should eventually be able to cruise with your board.
I'm not saying this is fun or easy but this is how you develop the correct timing and coordination between your kite and board skills. The payoff is awesome for the future and if you keep at it you just might find yourself enjoying more sessions on the same kite while others next to you have to stop and change kite size.
With the right technique and skills many kiters out there could achieve the exact same results with 2m less in kite sizes and sometimes much more than that and that's because they are used to being ''well powered'' not to say ''overpowered'' all the time since the beginning and never bothered practicing in lighter winds. Smaller kites are much more fun to fly and cheaper as well.
Good luck
Christian