To help address your query, please provide us the error message the user is getting. Also let us know the Time off type the user is using to book the timeoff. Provide the screenshot of the Time off policy setup for that Time Off type (Go to Administration > Users > Edit this users profile > Time Off tab.
Likely causes include issues with Time off policy which will be blocking the user from booking time off. Or user may have already booked a time off and may be trying to raise a time off on a holiday.