Was just watching a game and saw the following:
Trailing 14-7 with 90 seconds left in half. On opponents 25. Team keeps taking timeouts. They eventually score a TD to tie but leave over a minute on the clock. Then, when the other team gets the ball back at the 30 with a minute left and doesn't use any TO's or try to score.

Doesn't seem to be wise timeout usage by either team.

The timeout logic at the half is really loose and doesn't have the same logic as the end of the game. They do speed things up a bit to score but they're a lot more conservative. Most of the hardcore logic doesn't kick in until 4th quarter.