Kavod HaRav: If hypothetically someone is so busy in the month of Nissan that they dont feel like eating much on a certain day but theyre not trying to do a fast for atonement or teshuva; for example what if they are not feeling particularly hungry that day can they skip eating and/or drinking for a long time?
Shalom U'vracha, On Rosh Chodesh, the Mishnah Brurah writes that one should not fast even for one hour-- if it is a fast done on purpose. However, If one is fasting, but it is not done for a purpose (for example, he just is not hungry) he is allowed to fast for part of the day. However, he must not fast for an entire day. Even the eating of fruit would suffice. (Mishnah Brurah 418:2, and Biur Halacha, there). On Shabbat, the Mishnah Brurah writes, that one should not pass the sixth hour of the day without eating, even if he doesn't have intention to fast (288:1). I believe that these halakhot apply to fasting on Nissan as well (although on Nissan it is only a minhag and not as severe as other fasts done on joyful days such as Shabbat and Rosh Chodesh). Conclusion for Nissan: 1. Even one hour of fasting is forbidden if one is doing it intentionally. 2. If one isn't intentionally fasting he should not pass the sixth hour of the day without eating (around 12:45). 3. Even eating only fruit would suffice to fulfill the minhag of not fasting.