How to check success status of opened URL in Tasker? In Tasker, I have created a profile to open a URL when I visit certain place during certain time. It works.. When conditions are met, my default web browser (Dolphin) is opened to handle that URL visit.

I have setup another profile to kill Dolphin when I leave that place or time duration ends (whichever comes first).

Now, I want to make logic flow more complex: If URL fails to load, don't kill Dolphin.

How to check that URL was opened successfully or not? The rest I can do by myself.
You could use an "HTTP Get" action to query the site.  The response code sent back by the website is stored in the %HTTPR variable.  So %HTTPR = 200 means the site loaded sucessfully.  You can then make the rest of your task conditional on that variable, eg. IF %HTTPR = 200 THEN Go Home (or however you are "closing" Dolphin).  I know that %HTTPR is dependent on the mime type of the HTTP Get request so you'll have to tweak that a bit, and you may choose to look for different response codes to trigger different actions. 

There's probably other ways to do it but it would depend on the site you are trying to reach.