Should "request-after-request" be hyphenated?

hyphenation open-vs-closed-vs-hyphenated

No, hyphenation is definitely wrong in that context. Hyphenation is used only when the word becomes attributive.

Related

Hyphenating a compound noun in conjunction with '-related'
Less-experienced vs less experienced employee
Nonstop, non-stop, or non stop? [closed]
Hyphenation of -oriented when preceded by two words [duplicate]
How to capitalize a word with an adverb separated by a hyphen in a title [duplicate]
When is it correct to use upper case letters for nouns that may only be unique in a given context?
Should a name that is capitalized contain a lower case letter, for example, McDONALD or MCDONALD? [closed]
Question mark followed by a comma or semi colon in a list
Is there an English word for "fargin"?
Etymology of "chatterbox"
Usage of commas with "albeit"
The pronunciation of 'Hawaii'