go down vs fail

go down and fail both are verbs.

Word	Noun	Adjective	Verb	Adverb
go down	No	No	Yes	No
fail	No	No	Yes	No

As verbs, fail is a hypernym of go down; that is, fail is a word with a broader meaning than go down:

Other hypernyms of go down include break, break down, conk out, die, give out, give way, go, go bad.

go down (verb)	fail (verb)
grow smaller	stop operating or functioning
stop operating	deteriorate
be defeated	prove insufficient
be ingested	disappoint, prove undependable to; abandon, forsake
go under	become bankrupt or insolvent; fail financially and close
disappear beyond the horizon	be unsuccessful
move downward and lower, but not necessarily all the way	fail to get a passing grade
be recorded or remembered	fail to do something; leave something undone
	judge unacceptable
	be unable
	fall short in what is expected