I downloaded Frostbite sometime in January and installed it, but kept running into problems on the first mission (campaign, off-line play). I was moving troops into the village, where there was an enemy tank, and the whole game booted my out to my desktop (Win XP).
I went back in, started the campaing again, and again upon entering the village I did a Quick-Save (shame on me...) and a few seconds later a message flashed on my screen "All soldiers killed..." or lost or whatever.
I wasn't under fire, I was still looking through my eyes, and my character box on the bottom left of the screen said I was still crouching, so it didn't look like I was dead... so I did a Quick Load and the "All soldiers lost..." message came up immediately this time...
So I started the campaign over again, figuring I shouldn't be using Quick Save anyways, but when I got into the village again, and saw the enemy tank again, I was booted back out to my desktop.
When I played Frostbite, I launched it through GR as usual and never had any problems.
From memory though, I think there's a patch out for Frostbite. I don't know what issues the patch addresses, but it's always worth making sure you've got the latest version. Perhaps that'll solve your problem if using the dedicated Frostbite launcher doesn't...