From all the Biblical references – Old Covenant and especially New Testament, all I see as far as the issue of fasting is concerned is that people eliminated food as they intensely focused on God, often times while seeking guidance before making a strategic decision. In 1 Corinthians 7, marital sexual relations are yet another thing that some people chose to eliminate, along with food, for a period of time:
1 Corinthians 7:5
5 Do not deprive one another except with consent for a time, that you may give yourselves to fasting and prayer; and come together again so that Satan does not tempt you because of your lack of self-control.
In our day, you can add to that list any of the distractions of the modern age, and if you take out some time to intensely focus on God – usually focusing on a specific aspect of your spiritual life or when faced with a strategic decision to make – you simply postpone or eliminate those for a time.
For a lot of professionals, when you work on a project that demands intense mental focus, skipping meals is quite normal. It’s the same principle here. On a more permanent level, some people with very demanding vocations chose to stay single. They just don’t have the time to function as one should in marriage. That’s the reason Paul chose to stay single. It’s all about mission, focus, and making the most of your time. I am purposely giving some “secular” examples, to help us see simple non-religious parallels.
You must understand also that in the Middle East of then (and even now, to a large degree) eating is a communal event, there’s preparation, guests, and all those other activities, so it’s not a fast-food 15 minute proposition. Fasting eliminated not only food, but all that as well. At some point, even the original apostles got into communal activities revolving around food to such as extent that a large portion of their time was consumed with “waiting tables” – see Acts 6. They had to appoint people to take over communal meals aspect, so that they could re-focus on word and prayer. Instead of choosing to not eat, they chose to delegate that part, in order to eliminate the distraction factor.
With that said – oddly enough, Jesus not only didn’t food-fast during his earthy walk, but also defended his disciples for following his example of not food-fasting. And he was one intense guy with one intense mission.
So it all depends on what you want to accomplish by any form not eating, abstaining from marital sex, etc. One thing that we should not do is follow someone’s prescription without understanding what problem that prescription is trying to solve. It’s not what we do that should drive us, it’s why we do that’s important and that will determine the right tool for the job. Here’s an example with fasting, of people wrongly choosing food fasting, sackcloth and ashes to solve their problem (also notice how in v.3 they expected to wrangle concessions out of God by that), and how God expected them to apply an entirely different solution to the situation:
3 ‘Why have we fasted,’ they say, ‘and You have not seen?
Why have we afflicted our souls, and You take no notice?’
“In fact, in the day of your fast you find pleasure,
And exploit all your laborers.
5 Is it a fast that I have chosen,
A day for a man to afflict his soul?
Is it to bow down his head like a bulrush,
And to spread out sackcloth and ashes?
Would you call this a fast,
And an acceptable day to the Lord?
6 “Is this not the fast that I have chosen:
To loose the bonds of wickedness,
To undo the heavy burdens,
To let the oppressed go free,
And that you break every yoke?
7 Is it not to share your bread with the hungry,
And that you bring to your house the poor who are cast out;
When you see the naked, that you cover him,
And not hide yourself from your own flesh?