iPad mini Home button won't play nice.

I have an Applecare replacement retina iPad mini. The home button is less responsive than any of my other devices. With a normal soft push, my other devices spring into action, but with my RMini it takes a jab, but not always.
I took it to a genius bar appt 4 months ago, explained my problem and the guy took the device and jabbed it 3 or 4 times and handed it back saying there was nothing wrong with it.
I'm not used to jabbing my kit and the biggest problem is this mini is the device I use. Always.
I have a bad connection in my home button that drives me nuts. I don't want to use up my second Applecare replacement.
Would calling AppleCare work?
I'm really tired of trying to close an app but getting the effect of double clicking instead.
I was waiting on the iPad Mini 3, but since it is not an upgrade, I'm keeping my favorite device. How can I get Apple to replace this?

I have a relative in the hospital so I must go sit there the rest of the day today - however if I have a chance I'm going to call AppleCare and see what they say. I'll post their reply after the call.

Dlanod said:

I have the same problem on mine - from new. Took me long enough to get one with a decent screen hence I'm keeping it for now.

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I called AppleCare, they were super nice. My first contact sympathized with me stating she has the same exact problem. I told her the Apple genius did jab the button to make it work every time and she said she understood, but couldn't do anything at her level so she booted me up to a supervisor. Who said there would be not problem replacing or repairing the unit, but first I needed to do some stuff.
After running a diagnostics she said that 'backboard' was eating my memory and that could be the problem. so, wipe the device and set it up as now.
I have, no change. I've to to tell her that at 6:30 pm on Monday, at which time, she will order a replacement. So we shall see.
More to come......

You are absolutely right. Just another stall tactic on their part.
I'm suposed to wait for her call on Monday at 6pm but may call today if I get a 'hospital watch' reprieve.
I have an older relative that's not playing nice with the nurses LOL, so in kinda hamstrung.

haruhiko said:

I think the hotline guy was still trying to stop you from replacing the unit. What does an app have to do with your faulty home button? I would insist that's a hardware problem and request them to replace it immediately.

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After chatting with AppleCare, they diagnosed the problem and gave me some hoops to jump through. When finished, they made a Genius Bar appointment for me. I went in, the guy looked at the history with this iPad, and said to wait a second while he went to get me a new one. Finally, I've got a home button that works. This is a very good thing because I decided not to upgrade this time and will keep my (brand new rMini) for another year.