react-native-gifted-chat Can't show keyboard when have other text input in same screen

Question

If I have another text input on the same screen with react-native-gifted-chat component, the keyboard won't work correctly. It will appear in a sec then be dismissed immediately. Happens on both Android and IOS, physical devices and emulator.

I handled keyboard by myself, inside a KeyboardAvoidingView

Demo:

Here my code

<View style={styles.container}>
  <View style={styles.container}>
    {renderVideo()}
    <KeyboardAvoidingView
      behavior={Platform.OS === "ios" ? "padding" : undefined}
      style={{ flex: 1, justifyContent: "flex-end" }}
    >
      <View style={{ height: 350 }}>
        <GiftedChat
          textInputProps={{ onFocus: onFocusHandler, onBlur: onBlurHandler }} // 
          isKeyboardInternallyHandled={false}
          wrapInSafeArea={false}
          keyboardShouldPersistTaps="handled"
          onSend={onSendMessage}
          alwaysShowSend
          messages={messages}
          infiniteScroll
          scrollToBottom={false}
          inverted
        />
      </View>
    </KeyboardAvoidingView>
  </View>
  <AlertModal ref={alertRef} /> // This modal contain another input
</View>

Need some help making Keyboard for second text input works fine