Helium is a tiny little molecule that tends to escape through the walls of balloons, causing them to become non-boyant and sad. Normal rubber balloons usually die overnight, while the more expensive "mylar" balloons (which aren't really mylar at all, but usually a nylon/polyethylene double-layer film) gradually lose their helium over the space of a couple of weeks, become shrunken and ill before finally sinking to the ground, dead.
But the life of your favorite balloon can be extended indefinately by the sacrifice of its less-loved brother and sister balloons, if you preform Helium Transfusions!
Step 1: You Will Need
You will need the balloon you want to preserve, a sacrificial balloon to provide helium, and a long hollow tube of some kind that is small enough in diameter to be shoved up the valve stems of the balloons. I think the tube show here is from a kid's pinwheel. I've also used a piece of insulation from a cat5 cable, an SMT IC tube, and a fiberglass kite spar. A soda straw tends to be a little too short, and a little too fat, but you might get one to work.
Step 2: Drill for Helium
Most "mylar" helium balloons have a built-in one-way valve that consists of a flat tube of plastic that extends into the body of the balloon. Gas flowing in expands the tube and has no problems. Gas trying to get out tends to collapse the tube, so no passages is possible. It works really well. Some balloons have an additional self-adhesive layer to seal the tube shut, in which case you may be out of luck.
Find the opening for the inflation value on the step (usually) of the sacrificial balloon, and shove one and of your transfusion tube gently through the valve-stem until it escapes the far (internal) opening of the valve. This is usually 6 to 10 inches. Now your tube is holding the valve open, and helium can escape through the tube (You should be able to feel some if you squeeze the balloon.)
Step 3: Inflate the Patient Balloon
Insert the other end of the tube into the valve stem of the balloon you are trying to save. You don't need to go very far up the stem on this side; the gas is going to be flowing the way that the valve is designed to allow. Now, holding both balloon necks to keep them from coming off of the tube, squeeze the sacrificial balloon, and helium show flow from it into the balloon you're rescuing. Keep squeezing until either the sacrificial balloon is as empty as you can get it, or the patient balloon is full and firm. You may have to repeat the last steps with several sacrificial balloons if your balloons are really empty.
Step 4: Recycle the Sacrificial Balloon
You can use the tube to suck the rest of the helium out of the sacrificial balloon(s), returning them to something resembling their initial uninflated state. If there's substantial helium left, amuse your friends and family by talking with a lung full of helium, and remember to occasionally get your lungs full of regular oxygen-containing air as well.
Once the balloon is fully deflated, it can be stored easily and saved for future occasions. It's probably not economical to rent your own helium tank to re-inflate old balloons, but once you've collected a whole bunch you can consider doing things like inflating them with regular air and filling your house/office/whatever-mates room with them :-)
You can also use this technique for deflating "collectable" balloons to save them (like those nice expensive balloons from Disneyland), and eventually for saving your favorite party balloon.
Step 5: Enjoy the Rescued Balloon
Doesn't it look happier now?