I was just about to write a complaint about this, but obviously others have been experiencing the same thing. I had the settings that you changed already, set before I reinstalled Airdroid. This is a new bug created with the updated version. I used to have it running in the background for days without it disconnecting--no problem!
Unfortunately, I have seen this sort of thing so many, many times over the years with both software and hardware. Somehow these companies come out with products that do what they like, but piss off the customer time and time again. I have had to insult to shame some companies and they still didn't get it. Others screen you out (like BlackBerry) and others wait too long to get with the program and go under or get bought out.
My basic message has been for the last few years: Techs may be smarted than you, but they lack common sense. Please have your product reviewed and tested by non-techs which represent most of the World.
There was another competitor to Airdroid that I used to use and will try their latest version. Even if you install the older version of Airdroid, Google Play will force an upgrade unless you have a table/phone that doesn't use Google Play.