Multiple app links not showing

I believe this is what the plugin is generating:

<script language="javascript">
<!--
if (navigator.userAgent.match(/iPad/i) != null) {
document.write("<meta name=\"apple-itunes-app\" content=\"app-id=836522588\">\n");
}
else {
document.write("<meta name=\"apple-itunes-app\" content=\"app-id=836522588\">");
}
// -->
</script>

This looks correct to me.

However, immediately above that I see:

<meta name="apple-itunes-app" content="app-id=, affiliate-data=, app-argument=">
<meta name="google-play-app" content="app-id=sphinx.afl">

I don’t know if you added this manually or have another plugin installed? But either way, Safari will probably look at this first and ignore anything after that. In fact, when I open the site on an iPad I see the app banner appear and then immediately disappear.

Safari will only display a single App Banner for an app.

I suggest you either manually remove the lines in your template or disable the other plugin.