Because it's "coming off," it's likely broken or loose. Do not attempt to operate the vehicle until this is repaired. A broken or loose bracket can cause the alternator belt to come off, leading to alternator failure and potentially other serious problems.
You should take your vehicle to a mechanic for proper diagnosis and repair. Describing it as a "little elbow piece" isn't precise enough for them to know exactly what part it is, but they'll be able to identify it upon inspection. Bring photos if you can.