F# async function containing while loop with async calls fail to compile

You can't end a block with a let!, there has to be a body after it; that's the reason for the syntax error.

The message you're defining on the last line is a different variable to the one tested in the while condition. It seems you want to mutate the message; for that, you have to explicitly create a mutable variable:

let resendErrorsAsync (bus: IBus) (errorQueueName: string) =
    async {
        let! errorQueue = bus.Advanced.QueueDeclareAsync(errorQueueName) |> Async.AwaitTask
        let! msg = bus.Advanced.GetMessageAsync(errorQueue) |> Async.AwaitTask
        let mutable message = msg
        while message <> null do
            let utf8Body = Encoding.UTF8.GetString(message.Body)
            let error = JsonConvert.DeserializeObject<Error>(utf8Body)
            let errorBodyBytes = Encoding.UTF8.GetBytes(error.Message)
            let! exchange = bus.Advanced.ExchangeDeclareAsync(error.Exchange, "topic") |> Async.AwaitTask
            let! msg = bus.Advanced.GetMessageAsync(errorQueue) |> Async.AwaitTask
            message <- msg
    }