Just thought I would post my experience and solution here and hope it helps some:
My quick solution (so you don't have to read all the details): Disconnect TV and PC from wifi router and let the two connect directly. Screen Share uses Miracast and it is a direct wifi connection (no router needed).
Now the long story: I was having similar issues where I couldn't connect to my new LG TV (WebOS 3.5) with Screen Sharing and an all updated Dell Windows 10 laptop. Well actually I could, it would work about 5% of the time...that's 5% not 50% so it was very frustrating and most of the time on the failures the laptop would lockup and I would have to hold the power button down to shut the machine off. After reading some of the solutions here and reading some other threads elsewhere the thing that made a light bulb go on was when I read that Miracast is a DIRECT wifi connection between both devices...No Router Needed. So like some have suggested, I disconnected my TV from the wifi router and disconnected my laptop from the wifi router and let the two devices conduct their hand shakes and whatnots directly without a network router middle man. IT WORKED!!! Once the screen sharing worked I connected both devices back to the wifi network router and all worked great (except the LG TV did not remember the wifi password and I had to re-enter it).
Side note: I am one of the few people left in the world with a Windows 10 phone and the Continuum app on it connected 100% of the time regardless if either was connected to my wifi router or not. haha I love my windows phone, lack of apps or not it does what I need it to do...hope they follow through on the Surface phone or "Andromeda" phone or whatever it will be called.
Hope this helps some out there.