soldiers go through a bad spell now and then, too

This day is commonly spelled as Veteran’s or Veterans’, 

to imply the posessive.

However.

The United States Department of Veterans Affairs states the ATTRIBUTIVE as opposed to the POSSESSIVE is the official spelling because

“it is not a day that 'belongs' to veterans,

it is a day for honoring all veterans.”

Bonus link: va.gov/opa/vetsday/gallery.asp to see a gallery of 
Veterans Day posters dating back to 1978.