Most games automatically pause and save before releasing the switch to the browser, but Machinarium gets confused, launching the home screen, and forgetting the game state since the last manual save.
* iOS 7
Since the last manual save (from a save slot)? Hmm...it saves perfectly well on iOS 6—double-tap the home button when playing Machinarium, switch out to another application, then double-tap the home button again and select Machinarium, and it's exactly as you left it. But I don't have iOS 7 (holy cow, it's ugly), so I can't duplicate this. I agree with Alex about contacting the developers...making sure, of course, that you note that you have iOS 7 installed.