From 喘(あえ)ぎ (aegi, “連(れん)用(よう)形(けい) (ren'yōkei, “stem or continuative form”) of the verb 喘(あえ)ぐ (aegu, “to gasp; to pant”).”) + 声(こえ) (koe, “voice”). The koe changes to goe as an instance of rendaku (連(れん)濁(だく)).
あえぎごえ • (aegigoe) ←あへぎごゑ (afegigowe)?