This issue was first raised in May 2012. It is now November 2014. In that time, we've had 3 admin responses (one of whom actually tried to justify it) but no action. I shouldn't need to use a 3rd party app just to stop this app from running in the background and I'm just thanking my lucky stars that I didn't enable Find My Phone. Not even the back button stops it for me.
I daresay, being able to exit an application if I want to is not a lot to ask. In fact, I would say it's quite standard. I can't help but feel that this issue and the lack of action to fix it is deliberate, especially given the fact that we had the option to stop it in the past. If this is the case, I find it alarming that you could want to force me to keep it running, especially given the permissions your app has and the amount of access you have to my phone. It's a shame because I was quite happy with Airdroid before I upgraded and this issue started happening for me, however I have no choice but to uninstall it now.
PLEASE fix this issue for the rest of your users. Hopefully, when you say it'll be in the next version, you actually mean it this time (unlike when you said it 2.5 years ago).