The only leave of absences that are regularly approved are educational , military, medical, and FMLA. Leave of absence for personal reasons such as vacation sometimes gets approved if you are going out of the country or across the country for an extended period of time. Think 4-8 weeks. Most of the time you'll have to use all of your vacation first and then they might grant you leave of absence for the rest. When I've seen someone be able to take an extended vacation they had to use their vacation and personal leave hours and then management agreed to not schedule them. That seriously fucks with your average hours if it's any significant amount of time though.
I have done the LOA for a vacation, I needed 15 days, almost three weeks or 3 work weeks. It had to be done, since I was going with or without a job to comeback to. I explained that I had to take every single day off since it was common for some ETL's to see someone had days off and schedule them for a shift on a day they would normally not work just because to "keep them on their toes." And you can't tell my husband who gets 5 weeks of vacation a year he can't spend three weeks of it in one shot. HR ETL nodded and approved it.
Or another way to do it, is separate time off requests.
Then you fall back to "My time will fill the shifts, since that is what its supposed to do"