Because in terms of intelligence he is worth more to them alive than dead. To capture a member of al qaeda and to be able to interrogate him and find others who also may be part of sleeper cells is very valuable.
To just shoot him dead, or let him commit suicIde, and all that potential knowledge is lost.
You have a short memory. The Iranian Embassy seige (the clue is in the name) probably the SAS's finest hour, there was a stand off of six days before the SAS went in.
The Balcombe Street Siege in London when the Metroplitan Police trapped members of the IRA in a house also lasted Six days before its successful conclusion.
But sorry, the OP was posted to encourage some French bashing and general snook cocking at our neighbours. And here's me confusing things by giving examples of when we have waited several days before ending a seige. Carry on posting about Human rights and the EU and the french surrendering (you can even quote Monty Python if you like).
how long should a siege last, going on some that have happened in Britain as long as it takes to take the person alive, as they obviously want to do in this situation.
I doubt they'll capture him alive. It looks like he's decided he's going to die but is dragging it out to see if he can kill a few more before he goes.