But talking only about the SD card, here's some guesswork.
Let's assume writing the file causes 256K of underlying media to be erased and written, even if the JSON file is much smaller. Some write activity is probably occurring due to updating the filesystem metadata (directories, file allocation tables, etc). The card also does some sort of media management internally. 256K of media actually cycled is sheer guesswork and perhaps pessimistic.
If the card is 32G size, and let's assume it has well implemented (ideal) wear leveling, then you could expect 125,000 writes to erase/program every underlying flash sector once. Wear leveling across a large storage device gives you a *LOT* of writes...
The next big unknown is the underlying flash endurance. It's not going to be 100K guaranteed writes like we get with NOR flash. Let's assume it's only 1000 writes before errors begin to appear. That would imply you can write the file 125,000,000 times.
However, the controller inside the SD card (probably) implements some sort of bad block detection and remapping. Maybe. If it does, you could expect to get more life from the flash. But how much more, who knows. Maybe 2X or 3X?
But let's go with the 125M writes estimate. In the "every few seconds" seconds scenario, that's 1200 writes per hour. If sustained, it becomes 28000 writes per day, or 10.28M per year. If the guesswork of 125M "small" file writes wears out the card, you could expect it to last about 12 years.
Of course, low quality cards might have controllers which don't wear level well (or at all) and they might also have second rate flash memory capable of less than 1000 program/erase cycles per sector. It's all a lot of guesswork.
But the general idea of writing every 3 seconds, sustained 24/7 forever, means you've probably got several years. If you write several times per second, your card might wear out within months. But if the writing is only once per minute, or if the writes are in response to human activity rather than an automated process that runs 24/7 for many years, I would imagine any good quality card will ultimately fail due to aging processes rather than reaching its flash write endurance.