Hey!
So I had this issue...until 5 minutes ago. I had to google for an answer on my iPhone because it was so frustrating on my Macbook as the page wouldn't load etc.
So I thought with so many people having success with the Captains solution, I thought I'd give it a shot - however this didn't work initially (removing the connection and re adding and ticking and unticking the 'show wifi status' box).
Next, I unticked that box again ('show wifi status') and clicked apply and started browsing without the wifi icon and low and behold - I had no issues...mind you it's been 5 minutes without any issues, but that's 4.5 minutes better than any uninterrupted browsing time I've had in the last year!! After a while browsing without the icon, i went back to network preferences and ticked the 'show wifi status' box and it's still fine!!
The only concerning thing is that the wifi icon/display still switches from 'Wi-Fi: On' and 'Wi-Fi: Looking for Networks...' every 2-3 seconds still...as it does with many other users on here...but my connection works fine now...so it could be a normal thing (on my macbook version: 13" retina display, bought in May2015 on Yosemite and now on El Capitan) as mentioned by users farmerSam and K Shaffer
I'm still unsure entirely how I did this, it could be that the Captains solution was correct and I just didn't do it properly initially, in which case, thanks haha! So give it a go...hopefully it solves a lot of peoples problems as I know how frustrating this is.