I've never had 3711 go below 1.000, but I've heard stories of it happening. However, if you're in the upper temp range like that, 0.999 correcting to 1.001, and you're in the potential range of 3711. I've had it go from 1.065 to 1.002 before.
Up Next: Bluebird Bitter Clone v3.0, Scottish 60/-, Rye American Pale Ale
Primary: Robust Porter, Kitchen Sink Brown Porter, Bluebird Bitter Clone v2.0
Souring: Lamebic, Flanders Red, Brett. C. Old Ale, Sour Stout, Brett C. Wild Bitter, Wild Cider
Polypins: Dark Mild
Bottled: English Cider, Belgian IPA, Spiced Winter Warmer, Malt Liquor
In the "cellar": Brett B. Tripel, Quadrupel, Tripel, Brett C. Oaked English Barleywine, Lamebic