Question:

What is some evidence that voluntary fasting should be discontinued (eating before maghrib) if one cannot continue on with his regular activities?

Answer:

The Prophet sallahu alayhi wa salam said:

الصَّائمُ المتطوِّعُ أميرُ نفسِهِ ، إن شاءَ صامَ، وإن شاءَ أفطرَ
The one fasting a voluntary fast is a trustee (ameer) for himself, if he wills he can fast or if he wills he can break his fast

[Graded Saheeh by Al-Albani In Adaab uz-Zafaaf pg. 84]

Shaikh Bin Baz rahimahullah said:
بسم الله الرحمن الرحيم، الحمد لله، وصلى الله وسلم على رسول الله، وعلى آله وأصحابه ومن اهتدى بهداه، أما بعد: فقد دلت السنة الصحيحة عن رسول الله -صلى الله عليه وسلم- أن المتطوع أمير نفسه، فإذا صام تطوعاً فله أن يفطر، ولاسيما إذا احتاج إلى ذلك، فلا حرج في ذلك، المقصود أن المتطوع بالصيام له أن يفطر سواءٌ في أول النهار أو في أثناء النهار، وإذا دعت الحاجة إلى ذلك من باب أولى، إذا أحس بشيء من الضعف أو دعاه صاحب له إلى وليمة عرس أو غيره وأحب أن يجبر خاطره وأفطر فلا بأس، كل هذا لا حرج فيه والحمد لله، المتطوع أمير نفسه إن شاء كمل وإن شاء أفطر

In the the Name of Allah the Most Beneficent, the Most Merciful. May peace and blessings be upon the Messenger of Allah, his famliy, and his Companions, and all those who follow his guidance. As for what proceeds:  the Authentic Sunnah from the Prophet sallahu alayhi wa salam proves that a person fasting voluntary fast is a trustee for himself. If he fasts a voluntary fast, he can break it, especially if he needs that, then there is no harm in that. The intent is that the one fasting a voluntary fast is allowed to break his fast, whether it be at the beginning of the day or during the day. If there is a need that calls for that, then it is more deserving. If he feels weakness or his companion calls him to a walima (wedding banquet) or other than that and his mind compels him to break his fast, then there is no harm. All praise is due to Allah, the one fasting a voluntary fast is a trustee for himself, if he wills he can complete it or if he wills he can break his fast”

[Source]

Translated by

Faisal Ibn Abdul Qaadir Ibn Hassan
Abu Sulaymaan