So the plant you have there is a Maranta leuconeura. I have one that looks just like it!
There's a couple things that could be going wrong. In general, here are the conditions it likes:
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It likes indirect light. I keep mine by a south facing window that has an awning cutting the harsh light outside. Additionally, I have it behind a sheer curtain.
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It likes to be kept in moist soil, and in a humid place. I don't let mine fully dry out before rewatering it, and I live in a place where the ambient humidity is often 60-80%. If you live in a dry place, water it often and maybe keep it in the most humid place with enough light (kitchen or bathroom is usually more humid)
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and this is key, it does NOT like hard water. I honestly think this could be the problem with yours given what you said. Hard water has a lot of minerals, and over time, they build up in the soil. The plant might have been fine with tap for months, but now the soil could effectively be too "salty" for it.
If I had this plant, I'd do one of two things.
Option 1:
- buy fresh potting soil
- gently remove the plant from its pot
- shake off the soil from the roots
- rinse and scrape off any residue on the inside of the pot
- replant in fresh soil
- water with RO/soft water from now on (see note below), keeping it moist, in whatever spot it already lives
Option 2:
- buy or obtain real reverse osmosis (RO) water (see note below)
- water the plant so thoroughly with RO that the mineral salts dissolve and are carried away. This means soaking the pot in a large volume (like more than a gallon) of RO water for an hour or so, or watering it so water flushes out the bottom 5+ times in a row. You can tell if you flush the minerals out because there should be no grey dusty residue left on the soil or sides of the pot!
- add a small amount of balanced fertilizer (like follow miracle grow instructions or something)
- water with RO/soft water from now on (see note below), keeping it moist, in whatever spot it already lives
As backup, I might also try and root a cutting (again, in RO water) just in case it still dies anyway. Hopefully with these efforts it will revive, though!
Note on soft/RO water:
If you are looking for soft water, don't use water from a water softener (confusing, I know). This is because water softeners for humans replace the minerals with sodium ions. In essence, water softener water is just as "salty" as hard water, it's just different salts.
Instead, try and get deionized (DI) or reverse osmosis (RO) water.
Ideally, this would come from an RO system, which is a common kind of in-house water filter. If you live by a college, you could maybe ask for some from their science departments (especially biology or chemistry). You can also buy it online and have it shipped to you, but this is really expensive, especially considering that the maranta needs so much water.
Instead, I would buy a TDS meter (available on Amazon for like $7). It's a little stick device that you put in the water and it tells you how hard it is. With this, you could test a few brands of bottled water (avoid "spring water", or "remineralized" water-- go for "filtered" or "purified") until you find one with less than ~30 ppm / ~75 µS/cm dissolved solids. My grocery store sells water in big machines out front that reads 15 µS/cm, and it costs $2.50/5 gallons!
Honestly, I cheat and get lazy sometimes with mine and water it with tap. You saw yourself how long it takes for the solids to build up, and watering it with RO dissolves some of those over time. It's not like tap will kill it right away, but these guys sure are picky! :)
also... if it dies anyway and you're heartbroken, dm me and maybe I can send you a cutting from mine :-) cheers!