the game has to be connected to XBL with your account otherwise you will lose all in-game progress, like coins, missions, purchased gadgets, etc. Only the unlocked achievements will remain unlocked. If you play offline (i.e no wifi or 3G connection and without sign-in to XBL, you will lose all progress, except achievements. This is the same on the Win8, you have to be connected to XBL but because a computer is always connected to the net (either wifi or wired), you don't encounter this problem. But on a phone that you take with you on the go, you have to connect it to the wifi or 3G before you play otherwise you will play offline. I guess the in-game progress is saved on the game's server or on XBL that's why you must connect the phone to wifi or enable the 3G before you play. I noticed this when I tried to play the game on the bus, no wifi of course and my 3G was off. As soon as I connected the phone to the 3G, signed to XBL and all my progress was there (unlocked missions, coins, bought gadgets/jet packs/clothes, etc.)
I encountered the coin bug once, so I quit the game and reloaded and it was gone.