I've Safari 8.0.6 with iOS 8.3 on my iPad, while debugging through Web Inspector on my Mac (10.10.3), the connection keeps on disconnecting (I don't see the device name under Develop menu upon disconnection) but can resume if I quit safari followed by a relaunch then I'm able to refresh and inspect remotely again.
There are a few things to try:
Open the iPhone simulator in Xcode and debug there with Safari Web Inspector.
Sidenote: Maybe you need to download the Safari Technology Preview
Settings > General > Reset > Reset Location & Privacy
With this configuration it seems to work right now.
iPhone X, iOS Version 12.1.3 macOS Mojave Version 10.14.2 (18C54) Safari Version 12.0.2 (14606.3.4)
Edit 2019.08.13
Settings -> Safari -> Advanced -> Check that Webinformation is toggled on.
It was suddenly toggled off and I couldn't connect via the Web Inspector. After toggling it on, it worked.
For other devices / versions, please read further down (Maybe you can decrease your build size).
EDIT: 2018.09.20
@Chet found out, the Web Inspector keeps disconnecting for too large JS files and map files
https://stackoverflow.com/a/52338231/4641479
Issue on Github:
https://github.com/google/ios-webkit-debug-proxy/issues/275
https://github.com/google/ios-webkit-debug-proxy/issues/274
I could confirm this on a real device with a production build (1.8 MB + 2.4 MB files), the Safari Web Inspector stays always connected.
Since for the development build it is not:
Before my web inspector very rarely worked and often just stopped working - but was still open. After the safari update the web inspector opens and closes immediately. If you encounter such problems..
This will work:
Safari: 11.1 (12605.1.33.1.2)
https://developer.apple.com/safari/download
macOS Sierra and OS X El Capitan (I assume macOS high Sierra is also supported)
Maybe you need to download the Safari Technology Preview
On your device go to:
Settings > General > Reset > Reset Location & Privacy
Source: https://forums.developer.apple.com/thread/87181
Open Safari on OS X If you had connected your iPhone device with an usb cable, disconnect it first. Now plug it in.
On OS X Safari go to:
Develop > Device name > Apply for development
Now on your phone there is a permission question. Choose trust and now you can choose the open tab on your devices safari and debug.
Now the web inspector stays connected.