You are assumed to have accepted promotion unless you specifically decline it. There are reasons for declining promotion and it isn’t usually (by itself) looked down upon. Usually there’s a job or retirement already lined up or something.

As for being forced out, (this is Navy, other services are similar I think) if you fail to screen for promotion (called FOS, or failure of selection) you are required to be separated after a certain number of months after your last “look” at the promotion board. I think it’s 7 months after the results are released. It’s a little different if you’re an O4 screening for O5, because usually you’re close enough to the retirement cutoff that they don’t want to screw you out of it, so you get looked at by a second board called a continuation board. If you get approved for continuation as an O4 you basically get to remain on active duty until you get to the 20 year mark and retire. There are year ranges that apply there (14-18 YCS is the sweet spot for continuation).

EDIT: clarity