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Skype's UI designers are in cloud cuckoo land, and should be fired. I've yet to see a clean, efficient & simple Skype client - they just DON'T know how to do that.
 
I'm in the same boat as you: I don't use Skype enough to warrant having it always running in the background, but (if there was no cost to it) I wouldn't mind being available for messages all the same.

And, I'm sad to say, there's fire, not just smoke. Even without a call active, the Skype app must remaining running in the background in order to keep you signed in, and this prevents the iPhone from sleeping as often / as deeply as it otherwise would. I'm not sure what the current effect on battery is, but ~8 months ago, it was significant.

To mitigate this, somewhat, the app has a "Go Offline" setting -- you set how long it waits after you close (but not force-quit) the app before the background process goes offline, and stops sucking power. The options are Immediately, 15 min, 30 min, 60 min, and Never.

I just did your test -- clever suggestion! -- and it confirmed that this is still Skype's mode of operation in the current version. While signed in on my phone and watching on my Mac (in another Skype account), I force-quit the Skype app on my phone. Less than a minute later, I saw myself drop offline -- well before my "Go Offline" period expired.

It's a shame that Skype doesn't make full use of push notifications, in the way that most other iOS IM apps do, to allow you to stay signed in and receive messages/calls without sucking battery by running in the background.

That’s a huge shame! And a dealbreaker. It’s insane to burn battery 24/7 with no good reason, when Apple’s Push service has existed for SO long.

Even if someone does use Skype enough to accept the battery drain while not on a call... why should they have to?

I have problems with their desktop software too.
 
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