I feel your pain. My Note 3 widgets will stay updated for anywhere from a day to a few days and then freeze all at once. Weather and clock, though I've managed to find two that don't. The Weather Channel widget and Rainbow Alarm Clock Widget both work without being affected. I, too, am a BeWeather Pro user and it got so bad I had to stop using it altogether. So I tried GO Weather EX Widgets. They worked for a little while, like I said, and would freeze too. I've tried so many weather and clock widgets on my Note 3 I lost count. With 4.3 they would stop within Hrs or wouldn't start at all. After the KitKat update, I added the BeWeather Pro and GO Weather EX back on to see if there'd be any change and was hopeful at first until they stopped at exactly the same time about 36 hrs later. However, rebooting gets them going again so while it's a PITA, they are working anywhere from a couple days up to just over 4 days is the longest, so I guess it could be worse.
I stopped by the Samsung Hub @ Best Buy about my son's s4 active & when asked how I liked my Note 3 I said I loved it except for... and he finished my sentence with 'your widgets not updating'. So obviously they are aware and/or have been getting a lot of complaints and requests for help. I asked for the solution, but he said as of right now there isn't one yet. He said he wasn't sure if it was going to be up to each Dev to figure out & release an update for all the widgets it affects or if there'll be a patch for KitKat. Whichever it is, it can't come soon enough for those of us having these issues. ;'(
Sent from my FABULOUS Note 3!