It's hard to say, as it looks as if it getting enough nutrients. It could be that the pot is too small for the plant variety. I've grown a number of chillies (some plants are 3+ years old) in small pots and although some do really well others don't.

You could try watering more or even putting it in a less sunny spot. It looks like it's next to a table so back it away from the glass a bit, on the table. Other than that it looks to be quite green and healthy.

Regards
Nick

madferret, Thanks for your response. I appreciate. Will try it. I hope I will be able to save my little friends!

If you keep it in a very small container you could easily over water it or under water it, If were you I would put it on a bigger container that would required less often watering.

Also can you tell if the plant have been already hardened... seems like as some sort of stress and it could be related to the direct sun.

Best,
Guille

The plants are completely indoor plants. They have been sitting on my window sill for the last month and a half. I want to start moving them out now, but feeling less confident with this recent development.

I've fed them with coffee grounds tea yesterday, and now I am waiting for the results.

Eggshells and coffee grounds will not provide the nutrients that your plants need.

The plant is under-potted, and most likely getting too hot. It looks healthy otherwise, although the tender leaves will need outdoor SHADE only until they are hardened off....which could take several weeks, at least, in your unforgiving climate.

Josh