I planted my mint plant from a stem and within 15 days new leaves were seen for which I was happy but in next 7 days the stems started turning brown and seems falling toward earth. What's the reason for the same? The plant get around 30 min sunlight in the day which is the limitation for me at the place I m staying.
Too big of a pot for starting seeds. In the garden this is very different. You've got capillary action to spread the water out quickly in a lateral fashion which means there is AIR in the soil versus total saturation. The soil drys out more quickly and is able to hold heat (better for germinating seed). You aren't using seeds just a stem of mint that is subjected to constant moisture and no air. Mint is so tough and hardy, you are probably loving it to death, grins.
Any pot larger than a 2" by 2" peat pot will drown your seeds. Also a bit of fungal rot to be expected because of this moisture. Propagating by vegetative means is the same but depending on the size of the leaf or stem/node chunk the pot is still proportional. A 2" chunk, or a 1-2" leaf with a chunk of stem/node will be good in a 4" pot. Just a leaf and petiole, 2" is better. Moist not wet. Potting soil not garden soil. Real grow lights.
You've used garden soil in a pot. Big no no. Always use bagged, sterilized potting soil for any plant in a pot. Have you put rocks or gravel at the bottom of the pot below the soil? This actually makes the drainage as bad as having no drain hole at all.
If these are grown from seed or are separate; get potting soil, little peat pots and a tray to hold them upright, fill 1/3 full, tamp down lightly or knock the bottom of the little pot a few times on a hard surface. Using a teaspoon spoon soil and roots out of the 'soup' in the big pot, go very slowly so that you are able to pull as many of the long roots completely out of that soil. You pull too fast and you'll rip valuable possibly viable roots. Whatever you pull out is what you'll have and just continue to the new peat pot with 1/3 potting soil (dry). Gently land your little plant into the peat pot. With one hand support the little plant with a feather touch to keep it upright more or less. The other hand grabs a handfull of potting soil, drop it around the little plant, gently press the soil down around the plant, shake it gently or pop gently on a hard surface to get rid of air pockets. Do this until the soil is 1/4" from the rim.
If these plants are from a single chunk of mint stem, use a 4" peat pot with potting soil. Knock as much soil off the stem that you can, leave the roots alone.
Put your plants under grow lights (minimum 400 watts) get the fixtures close enough to add heat but not burn or touch...4 or 6" above depending on the strength of your light source. You could use those compact fluorescents that replaced our incandescent light bulbs...for a week or so, so that you can go find a real grow light. If you want to grow herbs inside, you have to have light. When starting seeds light isn't necessary (for most plants) WARMTH, moisture, air are critical. When plants start showing green leaves then LIGHT is important.
Plants are designed to deal with night not constant light. They need to 'reset'. A window is fine but still not as reliable and efficient as a properly placed grow light fixture. Also needs air movement. A little fan would really help to make the environment as unfriendly as possible to fungus, there is already a wet environment you've transplanted with a teaspoon that is full of fungal spores. Water sparingly and allow to dry a bit before watering again.
When these plants become vigorous you will then want to think about fertilizer be very sparing, less is better than more (Osmocote extended release 14-14-14 works well and you don't have to worry about fertilizing more than 3 or 4 times per YEAR). When you see the roots growing out of the bottom and sides of the peat pots, up pot them to 4" peat pots. Take the peat pot off the root ball, gently pulling it off without ripping roots too much. Yeah, those pots are meant to be planted right in the soil in the garden but they still inhibit root growth into the new medium whether it is up potting in fresh potting soil or in the garden soil...
If these little plants don't make it, throw all the pots, soil and the diseased little dying plants in the compost pile. The fungus they have is common and found in all non-sterilized soils anyway.
Get clean little peat pots with fresh potting or germination soil or you can use the expanding 'discs' that come with a tray made to hold each little 'pot' in place. One seed per pot. Domes really help keep the environment moist, warm. I always use fans, night and day for ventilation. Proper light. Warmth. Moist, not wet.