The Drop Kick

A drop kick was originally done as a suprise move (on 1st, 2nd or 3rd down - not on fouth down) just like a quick kick. Usually near the end of a half or game, when time is running out and your team is only down by 1-2 points.
I would think the reason it is not done anymore is field positon. If you are close enough to consider a drop kick, chances are close enough to make a regular (more accurate) field goal or continue the drive and score a touch down. If you are attempting a real long drop kick and miss your team gives up valuable field position.

Something else very interesting about drop kicks I found on the web, I am not sure if it is true?

Because it's there, in the NFL rulebook. You can look it up: Fair Catch Kick. The receiving team may call for a fair catch and promptly attempt to drop kick a field goal. No tee permitted, the rulebook asserts. That legislation probably gets covered under the Carrying a Concealed Kicking Device bylaw, but the NFL authorities can never be too careful, ya know.

The late Dallas Cowboys coach, Tom Landry, is believed to be the last to test the Fair Catch Kick rule. That was in an exhibition game. That was back in the dark ages, almost before cable.

If you watch Rugby you'll see guys nail these kicks from way out. I guess it's all technique.

Yea but there ball is a cross between a soocer ball and our football. Witch makes it better to kick.