#69242
No, ketosis will remain as long as your carb intake is below a certain level that will trigger your body to burn fat as fuel instead of carbs. People can eat every day and be in mild-medium ketosis as long as about 60-90% of your calories are fat and protein... With the remainder coming from carbs.
Do you have a reason for fasting?
Do you have safe realistic goals for your fast? If so your patents should come to the party. If your parents have good reason to worry you should listen to them and pay heed. Opt for a gentler way to maintain ketosis.