A pic of the plants and set up would really help as I am having a very hard time picturing your problem. What kind of soil are you using? Are the bags on the ground?

SCG

Lots of questions. Starting with where you are trying to grow them - what country, what climate? Secondly why are you sowing in a plastic bag? Thirdly does the bag have drainage holes? Fourthly what is the temperature?

Okay, the details:
I live in Indonesia, currently in rainy season, so rain is almost every day. Temperature range is 25-28 degree Celcius.

I'm sowing in plastic bag because i have a rabbit in the garden and don't have pot container left and don't want my rabbit to eat the seedlings. It's just until the plants are mature enough that i can put it in the garden. The plastic bag have drainage holes. Oh, and it's not on the ground.

For soil, i use a mixture of soil, cocopeat, perlite, and vermiculite.

As for photos, I'll try to photograph it later this morning. Thanks for helping :)

here the photos

If it's raining every day, you nast might be getting overwatered. The leaves kind of behave in the same way if they are overwatered or underwatered. I would guess this is the most likely problem

Your soil might have too much peat, and nasts don't always like that. The soil might be too rich for them.

With how warm it is by you, might be a bit too warm for the nasts comfort.

The dying back leaves might be old enough to naturally be dying off, though I'm kind of doubting that one.

I don't see any bugs in the pics, but even a little bit of bug action can make leaves die off.

And have you had problems before with the rabbits eating your nasts? Nasts are reputed to be hated by rabbits, and for sure in my garden they are one of the few plants the rabbits will always leave untouched. You might be ok to just go ahead and get them in the ground.

I agree with beesneeds, even my special deer that eat everything else that they are not supposed to won't eat nasturtium.

Methinks those plants are plenty big enough for the garden. I usually direct sow nasturtium.

I will leave the diagnosis of the chloritic and dead leaves to the pros.

SCG

i see, maybe it's overwatered. i never see any water puddle in the container, but i know that the container next to it -where i plant my cactus- has 2' water puddle in it whenever it rains.

i'll try moving the container to a sheltered place.

Oh, is it a problem if i grow the nast indoors? I have a 'sun' room where my iguanas bask themselves. It's just a room with transparent roof so the light can enter, though. However, I read that it makes the plant grows taller instead of bushier/wider/bigger?

Wow! That's so out of my experience...a sun room for the iguanas! How fun! You can sure try them in the sun room and see how they like it. You can cut off the dead leaves to promote new growth. I'm not much of an expert, but I liked reading this thread.

Well, everyone, thanks for the help! :D
I moved my nast to a more sheltered place a few days ago to see if it helps. Some of the leaves are still dying, but i'll just cut them off and see how the plants are after a few days more. :)
Will be posting here again to ask for more guidance if it still dying.