You need to manually block the click event from the bubbles, so it never reaches the top node (document), which closes the drop-down menu:
<div class="date-wrap pull-right" dropdown auto-close="outsideClick">
<button class="btn btn-info" dropdown-toggle>Date Picker</button>
<div class="dropdown-menu datepicker" role="menu" ng-click="$event.stopPropagation()">
<datepicker show-weeks="false" ng-model="dt"></datepicker>
</div>
</div>
Pay attention to ng-click="$event.stopPropagation()"
that does the trick.
: http://plnkr.co/edit/pPwW83Ro0u0g4dVhyZaZ?p=info