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Is it really not okay to just let a baby cry?
Literal
Baby [topic-は] make-cry as-is [object-を] do-is-not-good [conjecture-でしょうか]?
泣かせる is the causative of 泣く ('to cry') — 'to make/let cry.' ~たままにする ('to leave in a state of X') preserves an existing state without intervention. Combined: 泣かせたままにする = 'to let (the baby) keep crying.' The pattern ~てはいけない ('must not, is not allowed') negates the permission. Reads as a genuine parenting question.