Looks like the 3DS is here to stay, for now.
Nintendo in general are known to drop support for their older consoles as soon as their newer one is out- this has been true ever since the Nintendo 64 days. However, what people often forget in all this is Nintendo’s exemplary continued support for their handhelds even after their successors are released- the Gameboy Advance was supported well after the Nintendo DS was out, through to 2007, while the Nintendo DS itself saw support until late 2012.
This will, apparently, also be true of the Nintendo 3DS- if you were expecting support for it to dry up after the NX launches in March next year, then you would be wrong, according to this report by perennial Nintendo insider Emily Rogers. According to her, Nintendo plans on supporting the 3DS through 2018, or a full two years from now- meaning that by the time it is finally retired, the 3DS will have spent almost eight years on the market.
It makes sense from Nintendo’s perspective, since the NX sounds like it would be a premium priced handheld, and they would need something lower priced for their traditional demographic. Plus, as stated before, Nintendo have got a history of great support for their handhelds, too- so this report being true would certainly not surprise me at all.