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I was defending with a single Continental militia against a single Dragoon regiment in a Tactical battle. The battle lasted 2 turns then ended with a British victory even though no one had fired a shot. This has happened more than once. Any idea why?

The 5-1 rule.  It kicks in after the first turn.  See 32.11.  It seems to take priority over the rule requiring the attacker rout at least 1/3 of the defender (?)  At least thats the impression I've gotten while playing.
 
The dragoon must have had a strength rating 5x that of the militia, triggering that 5-1 rule on battle turn 2.

The Militia actually outnumbered the Dragoons. It happened the 3 or 4th turn of the game. I had a new militia unit in the town just north of Boston (I'm at work so I don't have the game up) and was attacked by the Dragoons that arrive as reinforcement on turn 2. The buggers chased me half way to Portland and we never fired a shot!!! [:)]

Yeah, I'm not sure how the game calculates "strength" but a freshly raised green Militia vs a Brit Dragoon veteran that enters as reinforcements...sounds like 5-1 could kick in.  Possibly.  To check for sure, the after battle report screen lists the strength power number of each side.