They didn't ask for his armband; he gave it up before they could.
Becks has never been the best player in the world, he was (and may still be) the most talented free kick taker in the world, which is quite valuable to the team. He's very good on the cross, but he's never been a complete player, nor one who could perform at 100% for the whole match. I'd compare him to Randy Moss (although without the arrogance). Good enough in spots that you have to leave him on the field, but not the best complete player.
Now that Aaron Lennon has proved just how good he can be during the run of play and Lampard has stepped up as an above-average free kick taker, the usefulness of Becks in wanning a bit.
I'm sure he'll still get his caps in, although he probably won't get the England record (which he's been gunning for from the beginning). There was a good point brought up earlier, that he is just barely back to form after the World Cup injury and maybe McLaren just didn't want to risk it.