Why were the British not able to take Boston after the battles at concord and Lexington?

Wow... well... I have no idea.  Boston was held by the British until March of 1776, almost one year after Lexington and Concord.

At the start of the war, the British held Boston.  The Battle of Bunker Hill was fought so they could have nearby Charlestown also.

Then the Continental Army besieged Boston.  After the Continentals got cannon after defeating the British at Fort Ticonderoga, they brought the cannon down and put them on hills around Boston.  This made it so the British had to leave.

But as far as right after Concord and Lexington, the British had Boston.