The See Invisibility spell and similar effects (Volo's Eye) can be contested. The enemy has to roll a dex saving throw and stays hidden if they succeed. Since the enemies who use invisibility are usually rogue types with high dex, they are quite good at it and likely to succeed if you have used the eye/spell/eilixir on a character with a low spell save dc.
Just as an added note, but as stated above, aoe s which enemies cannot save against, are a reliable way to force them out of invisibility.
