While I prefer to ride fully powered, Front Yards is often light (and close to home!) so I do get a lot of practice riding marginally powered. I approach the situation like this.
1. If possible, pump a bigger kite!
2. If I don't have a bigger kite, or I already have a kite in the air and just want to keep riding I'll get on a bigger board. For me that means a bigger surfboard or moving to a skim.
If I'm still stuck riding underpowered for whatever reason, here are some things that help.
First though, a description of apparent wind as it will play into how to maximize your kites performance.
While you are riding, your kite is facing into the wind and pulling on your lines. As you ride, your basically drag your kite along with you in the direction of travel by edging your board. This makes the wind speed your kite 'sees' higher than the wind it would see if you were just standing on the beach - ASSUMING you are going upwind at least a little, or your speed is greater than the wind speed when going slightly downwind. If you are going downwind your kite will see a lower wind speed. This becomes super important in a minute.
Imagine this... you are in a convertible, and flying your kite...(just imagine, don't try it!

) Say the wind is 20 mph. If you start to drive directly into the wind at 10 kts, the wind going by your kite is now 30 mph. Makes sense...right. Now suppose you turn arround and drive directly downwind at 10 mph. Your kite will 'see' only 10 mph.
Since the lift your kite generates is related to the speed of the air over it's wing shape, the faster the wind, the more lift it can generate. That lift is what pulls on the lines and drags us over the water. Since you can see that the faster you drag the kite through the air, the more lift you can generate by increasing the wind the kite sees, the secret is to get of on your board and going as fast upwind as you can. Once you generate board speed and start dragging the kite along with you it will create more lift than it would if you just stood still and parked your kite. If you are lucky, it will be enough to keep you riding upwind.
The other way to create apparent wind is to fly big power strokes thus making the kite travel through the air faster. These work well for water starts and short lulls, but a whole session of power strokes is tiring and no fun. Best to use them to get up to a speed where apparent wind takes over.
So how to put these concepts to use...
The hardest part is usually getting up on a plane and moving upwind. When underpowered, it's easy to pop up on the board and begin moving downwind for a short time before getting your edge set and moving upwind. Problem is that this will cause your kites apparent wind to decrease losing you more power and maybe even dropping your kite. Once this happens its often really hard to keep going.
The trick is to use a big bold power stroke to get up on your feet and IMMEDIATELY edge upwind. You will have to throw another couple of big power strokes (or downloops if you can!) to get up to speed quickly. You want to start dragging your kite along right from the start to generate apparent wind. If you don't edge upwind right away you will ride toward your kite and get slack lines and loose power.
Once you are up and riding, try to build and maintain as much board speed as you can. If you find that you can't ride through the lulls with just apparent wind you will have to use more power strokes to keep going. As you power your kite downward, edge upwind and as your kite drifts back up, flatten out your board a little and sheet out slightly, then sheet in again and dive the kite. Repeat as necessary.
When underpowered, remember that as you gain speed, you create even more lift that translates into more speed, but as you lose speed you loose lift and that causes you to lose more speed. It's a challenging balancing act but you will find that you can ride in some pretty underpowered situations with practice.
Hope that helps.