There are cases when the Datepicker component will not show up, it will be hidden after another element in the page.
In this case you will probably want to change the z-index of the datepicker element. No need to change the source css/javascript code of the component.

This is how the Datepicker works: it takes the z-index of the input it is applied to and increases it by 1. If your html input does not have a z-index then it will be considered to be 1 and it will be increased to 2.
If the element that blocks it will have a z-index higher then 2 the it is probable the datepicker cannot be seen.

To solve the problem you just have to put a z-index on the input higher then the element that blocks it from being seen.
For example:

<input type="text" style="z-index:101; position:relative;" />

Why did I use position:relative? Because otherwise z-index is not applied. Z-index is ignored in a regular static flow, it has to be relative, absolute or fixed.