There are two reason that might happen.
-Before you enter a dungeon, your mercs must be told to enter any fights you will encounter with the 'engage' button. You can view it from the Hero screen, as shown below.
-Once you enter the dungeon, you need to choose which mercs will enter the dungeon with you. The other mercs will sit at the entrance and await your return.
It's possible that when you bought your new merc, you didn't tell him/her to engage in battle. By default, it might not be selected.
Hope that helps.
