While this rarely if ever happens servicers are not required to grant forbearances. The only reason there is usually a denial (outside of criteria not being met) is that the borrower is out of time. However a servicer does not have this option for what is called a Mandatory Forbearance. These are exactly they sound, they are mandatory and if a borrower qualifies they cannot be denied.
There are three types of forbearances. The three are the Internship/Residency Forbearance, the National Guard Duty Forbearance, and the Department of Defense Forbearance. We have went over what these forbearances do in other areas (just follow the links!), but to quickly recap:
Internship/Residency: Used to cover doctors, dentists, etc while having official required internship or residency work
National Guard Duty Forbearance: Used if you cannot qualify for the Military Deferment but was called into active duty by your state or the federal Secretary of Defense
Department of Defense Forbearance (use above link): Used to keep account current until DOD makes agreed upon payment towards student loans
For what we are talking about what these forbearance do are not as important as the fact of knowing your rights as a borrower. If you meet the criteria for any of the forbearances above, they are required to apply these to your account.
If you have any additional questions it is best to either speak with your servicer about the forbearance itself or the certified official (such as a commanding officer for military) about the corresponding program.