Due to the water changes, you keep restarting your cycle. You need to use a product like ammo-lock. Ammo-lock will neutralize ammonia to fish but keep it so nitrites can eat it.
neon tetra's are not the best choice for cycling, which no fish are, some fish are just more hardy.
The water in an established tank is contains very little good bacteria. The gravel or filter media is something that will speed up your cycle.
I find it wierd that you have no nitrites. Ammonia is generally what live plants will eat, even when an abundance of nitrates are present.
TSS has generally 50/50 chance of working from what I've heard on the forum. Always have a backup cycling method present.
One last thing, I would take the plants out. They
MIGHT be the
nitrite problem.