Yes, as it releases tannins it will eventually run out and be useless. Depending upon your water hardness (and corresponding pH), more or less will be needed to lower the hardness/pH to the desired level. You don't mention the hardness and pH of your source water (tap presumably) or the aquarium, so I can't say much more on that.
Of the two fish you mention, the rasbora Trigonostigma espei while certainly preferring (and thus doing better in) soft acidic water will adapt to slightly basic medium water. The acceptable range is given in our fish profile [click on the shaded name, or access profiles through the tab second from left in the blue bar above].
As for the Green Neon Tetra, Paracheirodon simulans, they are much more sensitive. This fish is still wild-caught as far as I know, and they occur in many of the waters of the cardinal tetra. Again our profile gives the preferred range for this species, and it is very soft and acidic. Their habitat has a pH of 3.4 to 4.8 and zero or near-zero hardness. But the aquarium need not be that extreme, as noted in the profile.
If your source water can be lowered to these levels (assuming it needs to be) the fish will be fine. I'm assuming the platy will be gone (parent and fry) as they will not manage in such soft water. And I agree with Tyyrlym's advice on smaller water changes to lessen pH shock. And these fish need plants, even if only floating to make them feel secure; they are not fond of bright light.