Well that didn't last long. Just a couple of weeks ago, Verizon launched a new update for the Samsung Galaxy S3. It was supposed to offer a number of bug fixes. Although it did do that to a certain extent, apparently it also introduced a number of new issues so Verizon just yanked it. Shortly after its release, a number of users experienced poor LTE connectivity and decreased battery life issues. Verizon and Samsung are now working together to address these issues. Here's a quote with a few more details,

No time frame is given for the fix. Until that happens, there is a solution that has worked for some users. Go to Settings > More Networks > Mobile Networks on your S3 and change the network mode to LTE/CDMA instead of Global. If that doesn't work and you've already installed the update, you'll have to wait and hope that the fix comes quickly.

Are you a Verizon Samsung Galaxy S3 user? Have you experienced the 4G LTE connectivity issues?
Source: AndroidAuthority