I have seen some players quickly increase their ELO within months, and some within years. Is there some genetic intelligence in those players (like someone in their family also played chess)? I ask this because my tactics (blitz) rating is not improving. I did about 3000 puzzles this month. After 2500 of them, I can't get past ELO 1560, and that's why I'm thinking about leaving chess. Is there really a natural gift?
Different people have different abilities for chess, just like for any other activity. Some people are "gifted", others aren't. Your chances also diminish with age, but almost every human can make it past 1560 (or 2000 for that matter)
That being said, you won't improve much in just one month. Consistency is much more important than intensity. Try making a reasonable amount of puzzles every week rather than doing thousands of them one month only to burn out for the next.
Also note that tactics skills are the most important aspect you need to train, but not the only one. Have you tried contancting a coach? Even if you can't afford it on a regular basis, it may be good for you to book a season and define a training plan.