They're very probably binding the pistol to Connor
By somehow, I was really lost my pistol after they stick on Connor's hand and go to play around. But sadly, as same as Ubisoft binding the blowpipe to Edward in AC4, even you can get rid of your pistol, they will turn back to Connor after you change your outfit. I didn't test it yet but I guess fast travel either.
I don't know why they wants to binding the pistol to Connor, that makes no sense because we can so easy to get them back from shops and home.
It took me a while to realize what you were doing in this one, but I do love the final comment.
"It must be one of the most difficult challenge in human history to have a function to allow players to choose to carry weapons or not."
“Force has no place where there is need of skill." Herodotus