Hi TTD, unless she is absolutely determined to find help and work out why she inevitably ends up bingeing, you're looking at your future going through this cycle with her. It makes the time between binges stressful as well because you're waiting for the shoe to drop.
She doesn't have to be declared an alcoholic to be treated if she's determined enough. She can go to a private therapist or AA for instance. If she doesn't it sounds like she'll gradually deteriorating for the rest of her life.
As for you, as much as you love her you'll have to decide whether you can stick this out indefinitely. I don't suggest an ultimatum to force her into treatment because she has to do it because she really believes she needs to for her own reasons.