Why can't I post to Twitter from Safari in iOS 7?

I just bought a new iPhone 5S. The first time I set it up, I used iCloud. When I tried to post to Twitter from Safari (via the "share" button at the bottom of the screen), the app was unable to find my location, and the tweet appeared to send but was never posted.

I did a factory reset and set up the iPhone, this time without activating iCloud until I had set up Twitter. I was able to post to Twitter from Safari for a few hours, but after I configured iCloud and re-installed a bunch of apps, it stopped working again.

I have had a similar problem on my new iPad Mini.

Help?