The Dalish Elves, self-appointed custodians of the elven language and lore, use more Elvish than their city elf brethren.
The Elvish of the Dragon Age is thus a fragmented remnant, a few words that are thrown into conversation rather than a working language used to conduct everyday life.
When the elves settled their second homeland, the Dales, they aimed to restore their lost language and lore, but the Dales fell after an Exalted March declared by the Chantry in the early Glory Age. The Elven Language, or “Elvish”, was largely lost when Elvhenan fell to the Tevinter Imperium and its people were enslaved around two millennia before the Dragon Age.
