Assuming that your gears are adjusted properly, there is another thing to remember/consider. When the gearing is under load (as in, you are putting force on the cranks to move the chain ring), it is much harder to shift the front rings than the back ones. This is because the front derailleur is attempting to pull the chain off the ring at the point where the forward force is the greatest. This is often why people drop their chains on uphills. You are basically trying to apply force to the same spot in two different directions at once. The derailleur is trying to force the chain to the left while the chain ring is trying to force it forward, at the same time in the same place! The best thing to do is to get into the correct front ring BEFORE you need to apply a lot of force to the cranks. If this means shifting into the smaller ring on the downhill way ahead of time until you get the hang of it, then so be it.

The rear derailleur will work better under these conditions because its much easier to move the chain latterally from the underside even when under force from the cranks. Plus, at the rear, the chain is moving the gearing, the gearing isn't pulling the chain, so the physics are a bit different.

Basically, get into the correct front ring before you need to pedal to keep going up the hill and then from that point on, use the rear gearing to make adjustments as the incline gets steeper (or as you get tired). If you do need to shift the front ring - try to ease off the force you are applying to the cranks (maybe on a flatter spot?) and shift it then. Easier said then done when you are talking steep inclines!