Hi Woodwyn, I've been having the same problem, on and off. Here's what I've learned:
When this is happening, and hitting the Home key doesn't seem to work, I have to find the "sweet spot" to make it work. Sometimes it's just a little above and to the left, sometimes below and to the right. Just keep pushing on the edges of the button, all the way around until you find the spot that works. Then, once it's working, hit it there over and over - it'll keep switching between Spotlight and your Home Screen. That shows you you;ve worked out whatever kink was keeping it stiff.
I can usually go a few weeks before it happens again. On my last trip to the Apple Store, they told me if it's happening and I can duplicate it in the store, they'll just swap it out right there for me. But the problem has to be happening while I'm there to demonstrate it. So if you're near an Apple Store when it sticks, don't search for the sweet spot ... just let it be, take it, show them it doesn't work and they should swap it out. But, as always, make sure you've backed up your iPhone on your last sync with iTunes.
Hope this helps.