[EDIT] In some missions you are put from the briefing directly to combat, therefore you are unable to select / change your gear, on the other side you are starting the mission with weapon that is not in the armory (MXSW when attacking Mike-26 and MXM in the last mission - where you can enter the armory)
Also it is true that some items are not saved or are placed somewhere else than those 3 boxes in armory. For example PCML I brought is not there, but ammo for it is there. Also there is no option to take a bag even when you bring it from a mission.