Though perhaps not exactly what you're looking for, we have lost the ability to send manned missions to the Moon the way we did in the '60s and '70s.

That ability was based upon the Saturn V rocket, the heaviest lift vehicle ever made and to date the only rocket ever to lift human beings past low-earth orbit. It was also, perhaps, the most complex creation in human history. The various pieces, from the massive thrusters to the control ring to every inch of wiring, was assembled by NASA from parts subcontracted out to dozens of companies nationwide.

While this sped up construction rates, it also meant that once the Saturn V project shut down, only a perishingly small number of people knew how it all fit together.

Worse still, plans for every piece no longer exist. Scattered as they were to subcontractors, often enough a company would shut down, taking their blueprints with them. It's possible that somewhere, in the basement of some old retired (or dead) engineer, is an important blueprint for how a left-handed gozwanger fit into the entire Saturn V project (note: I made that item up), but nobody knows about it. Not even NASA has a full set.

As a result, we have lost the ability to send manned missions to the Moon as we did 40 years ago. To do so again, we would have to generate the skills and equipment from scratch.

References: Stages to Saturn, Roger Billstein / NASA History Office

Encyclopedia Astronautica: Saturn V

...and a lifetime of being fascinated by Space exploration and rockets. I'm a geek.

Some specific examples of lost technology I can think of are Roman concrete and Damascus steel. Roman concrete was made with a particular recipe that has been lost since the around the time of the collapse of the Western Empire in the 400s, the infrastructure required to gather the materials to make the concrete and the ability to fund large concrete construction projects both collapsed with the empire and so technology was lost. This concrete is actually more resistant to weathering than is modern counterparts.

Damascus steel was a particularly resilient form of steel that was also supposedly better at maintaining a sharp blade. The techniques to make it died around the late 1700s either because the trade routes that imported the steel to Damascus from India started to fail, or because the techniques were kept secret enough they were eventually forgotten.

The ability to make the rich blue color on stained glass windows, like the ones still seen at the Chartres cathedral, is often said to have been a lost technology. This theory has been popularized by Malcolm Miller, the premier English language tour guide of the Chartres cathedral and the author of several books about that master piece of High Gothic architecture. However, as this link shows, art historians now seem to think, this is really an example of losing the means to produce the deep blue color on the stained glass windows at Chartres, not losing the technology entirely. Modern glass is too pure and the recipes for making the blue stained glass have been found. Although, these recipes are not very clear. The terminology is murky and the exact measurement of the ingredients is not very clear. Chartres is a very poorly documented building. We do not even know the name of the master mason, that directed the construction of that church. It is a marvelous example of medieval stained glass though. 152 of the 186 large stained glass windows at Chartres are still the original glass. Amiens has none of its original stained glass windows and Rheims only has small portions of a few windows, that predate 1500.
http://artelisaart.blogspot.com/2012/03/secrets-of-chartres-bluehistory-of.html