In reply to gingerkate:
basically, you need more stamina. The advice to not rush up stuff at the wall, but climb more slowly is good advice.
Also, you should look at whether you are actually climbing efficiently. Lots of people who tire quickly when working out sequences are holding on too hard. It is amazing the improvement you can see if you learn to relax on the holds, and use the minimum grip possible.
Try this; when slightly below a bolt on a good hold get in a nice stable position and slowly relax your grip, and keep relaxing to the point where you actually fall off. Most people are stunned how little they need to grip to stay on.
Obviously it can be hard to do this once the nerves set in, but again that can be trained at the wall. Simply repeat the above exercise getting slightly higher above the bolt each time. Your body then gets used to relaxing when you are nervous.
Worth a whole grade for most people...