I'm another who gains during ovulation. Actually, I normally ONLY lose weight the week or two between ovulation and TOM.
So... I would say, though, if it's really an issue why not talk to your doctor and get a full check up. It never hurts and I wish I would've gone at the beginning of my journey just to ask some questions etc. If you're eating 1000 calories a day at your weight, you're going to lose. I don't know how sedentary you are but, honestly? 1000 calories a day sounds really low to me. I eat more like 1400-1800 a day and am 100lbs less than you and am still losing. I am pretty active but still, you might want to consider eating closer to 1500 (or at least check with a nutritionist first because again I don't know your activity levels).
Now, I do think it's totally possible to have stalls (I've had my share myself) but during those times I've always lost inches at the same time and normally I could point to something being different (for instance, during my first stall I had started heavy weight lifting, which is notorious for water retention).
But I really don't believe anyone is genetically predestined to be obese. If so I should be! Almost all of my immediate family members are obese, very obese for that matter. That being said I also have immediate family members (not blood relatives) who are too. I honestly believe it's much more about habits, food choices, exercise levels etc than genetics. Certainly, some people are more prone to gain weight (and I'll put myself in that category) BUT it's entirely possible to still lose it. Now, the weight loss might come off really, really slowly (like I said I've had stalls and many slow months) but it's still possible (excluding some diseases that do cause you to gain weight but again, that's why I suggest talking to your doctor). There are also those of us who are large framed and might not get to the low end of a healthy BMI but being large framed myself I can tell you that I have been within a health weight range before in my life and it's definitely doable.
I don't think weight loss is easy by any means. You need to find a plan that works for you both in terms of weight loss and ability to stick to it (that alone has taken me YEARS to find!) but I don't buy that it's impossible at all. Some people might have more struggles than others, certainly. Years of yoyo dieting can wreck havoc to your metabolism but it's still possible to lose. You might have to focus more on exercise and have lower maintenance calories than others because of it but it's still possible.
I would suggest tracking what you eat and weighing daily to figure out your patterns. Have you eaten more salt this week that caused a gain? Ovulation could certainly be contributing too. Did you start a new exercise program? What if you do calorie cycling (some days higher, some days lower), does that help? Take note of all these things with your food choices and find patterns.