I guess it’s commonplace to see a football team attempt a field goal on 4th down. Let’s say the football team for whatever reason decides to kick it on 2nd or 3rd down and they miss it. Does that attempt count as a down and therefore can have further attempts on making it?
The attempt counts as a down. However, the kicking team will not have further attempts on making it as possession changes, given that the field-goal attempt is missed as outlined in Rule 11, Section 4, Article 2.
If the field goal is blocked on third down, the 2012 NFL Case Book (page 62) suggests the following scenarios:
A.R. 11.43 MISSED FIELD GOAL—BEHIND THE LINE
Third-and-2 on B10. Team A field-goal attempt from the B17 is blocked and:
a) goes out of bounds at the B18; Ruling: B’s ball, first-and-10 on B18.
b) is recovered by A2 at the B15 who runs for a touchdown; Ruling: Touchdown Team A. Kickoff A35.
c) is recovered simultaneously by A3 and B3 at the B21; Ruling: B’s ball, first-and-10 on B21.
d) is recovered by A4 at the B19; Ruling: A’s ball fourth-and-11 on B19.
e) is recovered and downed by B2 at the B15; Ruling: B’s ball, first-and-10 on B15.
f) goes beyond the line and then returns behind the line, untouched by Team B beyond the line in the field of play, and goes out of
bounds at the B16 or is recovered by A2 at the B16. Ruling: B’s
ball, first-and-10 on B20.
Rule 11, Section 4, Article 2 (page 58) in the 2012 NFL Rule Book states:
Missed Field Goals.
If there is a missed field-goal attempt, and the ball has not been
touched by the receivers beyond the line in the field of play, the
following shall apply:
(a) If the spot of the kick was inside the receivers’ 20-yard line,
it is the receivers’ ball at the 20-yard line or
(b) If the spot of the kick was from the receivers’ 20-yard line or
beyond the receivers’ 20-yard line, it is the receivers’ ball at the
spot of the kick.
Note: These options apply only if the ball has been beyond the line.