Yes, I've tried that several times, too.
When I power down (with or without the cover attached) by holding the sleep/wake button down, and then swiping-right to power down, the iPad powers down, then immediately powers back up again.
And I have also done the hold-both-buttons strategy several times.
There seems to be no way I can make the iPad stay powered-down.
Not good for battery capacity!
That didn't do any good either. I' sure now that it's an iPad hardware failure. Several weeks ago, the volume control buttons stopped working ... Press them, and nothing happens. The folks at the apple store tried restoring the unit etc. etc. and nothing helped. They finally noted that the sound would still work if an external speaker is plugged in -- but ONLY if an external was plugged in. They told me that the motherboard was failing and that nothing could be done about it because the 1-yr warranty had expired.
So I' m sure this latest problem is just the next step in the slow death of the hardware, even tho the unit has never been dropped or got wet.
I guess I must just have got a lemon (I assume that not ALL IPads hardware start failing within the first two years).
I'll think about replacing it with a new one, but first I'll take some time to look at Android and Microsoft tablets, too.
As a last resort, I made a "genius" appointment at the local Apple Store.
They restored my iPad to factory-original state, then tried powering it down.
It immediately powered itself back up.
The Genius staff confirmed that yes, it is the motherboard that's bad and progressively getting worse. And they confirmed that there's nothing that can be done about it, since my iPad was beyond its 1-year warranty. I asked if I could at least get some kind of discount if I buy a new one, but alas, they said that I can't.