Yes, Apple has fixed this problem.
Apple has acknowledged the problem and is offering to repair devices that were manufactured with this defect. According to Apple, iPhone 5 models manufactured through March 2013 may be affected by the defect. You can go to Apple's support site to see if your device qualifies for repair and, if it does, to get instructions for how to get your phone repaired.
So if you have an iPhone 5 with a failing sleep/wake button, put the device's serial number into the form on Apple's sleep/wake button replacement program page to find out if you can get your device repaired free-of-charge.
Note that the device must have a qualifying serial number and must actually be exhibiting the problem to qualify for repair. I have an iPhone 5 device that was given to me in mid-April 2013 as a replacement for an early iPhone 5 device that suffered the sleep/wake button failure after about 6 months of use. The sleep/wake button on the replacement iPhone 5 has worked now for over a year and is not experiencing the failure. Even though I put the device's serial number into the form on Apple's sleep/wake button replacement program page and it indicated that my replacement device is eligible for repair, it probably won't actually qualify for repair because the button is working just fine. But it's nice to know that, should my current device also experience this failure in 6 to 12 months, Apple will repair it even though the device is otherwise out-of-warranty.
Some other caveats to note (from the replacement program page):
Apple may restrict or limit repair to the original country of
Your iPhone 5 must be in working order to qualify for this program.
If you believe you have paid for a replacement due to this issue,
contact Apple regarding a refund.
This worldwide Apple program does not extend the standard warranty
coverage of the iPhone.
The program covers iPhone 5 models for 2 years after the first retail
sale of the unit.