Bike fit is usually the cause when long climbs produce back pain. However, there are lots of "correct" fits. Some are more aggressive than others (lower handlebar, higher saddle) and are more likely to make your back hurt. So the first thing to check is that your "fitter" didn't go too far in that direction.
Even with a correct fit (for you and your style), long climbs can make anyone's back hurt. The muscles of the low back work harder during seated climbing as they provide support for the trunk (much as stron abdominals are needed for aggressive cycling). Usually, climbing during training will make them stronger. You have been doing too much climbing, for your level of training, and gotten ahead of the curve for your back muscles adaptation. The solution would be to cut back on your training expectations and stop hammering yourself before the event. Climb a bit less, and don't go all out.
You might also check your climbing technique. Alternating sitting and standing is key to relieving tension on back muscles.
And remeber those abs I mentioned above? Low-back pain can result from a lack or imbalance of midsection strength. Hard climbs put a whole new level of stress on your midsection muscles and may require extra abdominal strengthening work. Crunches and other abdominal exercises may be very helpful.
To see illustrated back exercises and stretches for cyclists, click http://www.cptips.com/www.rlaenterprises.com/cyclestretch, a site developed by roadie Rick Schultz.
*Credit to Fred Matheny from www.roadbiker.com for some of the content above.