Twitter Built-in Timeline Widget won't load tweets sometimes

I am using an embedded timeline widget on my website. I just copied the HTML from the widget generator and pasted it into my site. It works most of the time. But sometimes it doesn't display any tweets and just displays the text "Tweets by @xxxxx".

I'm not sure where the problem is. It is difficult to pinpoint exactly how this happens sometimes. Any solution would be greatly helpful. :)