Paginate events without setting expiry date
You need to include an extra parameter in your initial query to only fetch event entries for events in the future and remove the conditional test from the for loop.

Currently you are fetching all event entries and paginating those, but only displaying event entries where the eventDate is in the future.

Try this instead:

{% paginate craft.entries.section('eventsEntry').limit(3).eventDate('&gt;=' ~ (now | date('Y-m-d H:i'))).orderBy('eventDate') as pageInfo, upcomingEvents %}

{% for event in upcomingEvents %}     
...
{% endfor %}