попробовал ваш код с некоторыми данными.Работает нормально для меня.
import React, { Component } from 'react';
import { Image } from "react-native";
import { Container, Header, Left, Body, Button, Icon, Title, Content, Card, CardItem, View, Text } from 'native-base';
export default class App extends Component {
state = { events: [1, 2, 3, 4, 5] }
render() {
return (
<Container>
<Header style={{ justifyContent: 'center', marginTop: '4%' }}>
<Left>
<Button transparent onPress={this.handleBackButtonClick} small={true}>
<Icon name='arrow-back' size={30} color="white" />
</Button>
</Left>
<Body>
<Title style={{
fontSize: 20,
fontWeight: '200'
}}>Events</Title>
</Body>
</Header>
<Content>
{(this.state.events).map(event => {
return (
<Card key={event} style={{ marginTop: '2%', marginLeft: '2%', marginRight: '2%', marginBottom: '2%' }}>
<CardItem>
<Image source={{ uri: "https://nativebase.io/assets/img/front-page-icon.png" }}
style={{ height: 200, width: null, flex: 1 }} />
</CardItem>
<CardItem>
<Left>
<View style={{ height: '50%' }}>
<Text style={{ fontSize: 15 }}>Jun</Text>
<Text style={{ fontSize: 15 }}>15</Text>
</View>
</Left>
<Body style={{ alignSelf: 'flex-start', marginLeft: '-50%' }}>
<Text style={{ fontSize: 20, fontWeight: 'bold' }}>Title</Text>
<Text note>Description</Text>
</Body>
</CardItem>
</Card>
)
})}
</Content>
</Container>
);
}
}
Gif