Recognizing vs Deciding in defining class BPP
Complexity theory makes no distinction between "deciding" and "recognizing". The two words are used interchangeably. Turing machines considered in complexity theory are usually assumed to always halt. Indeed, usually only time-bounded machines are considered (such as polytime Turing machines), and these halt by definition.

In your particular case, you can interpret accept as halting in an accepting state, and reject as halting in a rejecting state. The Turing machine is thus allowed not to halt. However, the class BPP also requires the machine to run in polynomial time, that is, to halt in polynomial time. In particular, the machine must always halt.