In a recent interview with Kotaku, Reggie says that he hopes Nintendo will continue to sell the 3DS for 4 more years. That sounds nuts, and it is. But of these 4 years, how much longer can Nintendo keep the 3DS going. Once again, they still stick to the claim that the 3DS will continue to be supported in 2019 and that new software will be released for it. However, use the term "support" very loosely here. Of the 4 3DS games shown in September's Direct this year, only one new game was announced, Kirby's Extra Epic Yarn, a port of an 8 year old Wii game. This past year saw Nintendo slowly beginning to phase the system out. It's release slate has been slowing to a crawl, advertising is sparse and only promotes older titles, it was a complete no-show at E3 this year, 2 of its games were ported to Switch, its segments in Nintendo Directs are getting shorter and shorter, and this year's Nintendo Holiday Mall Tours have it regulated to a small, barely-acknowledged, kiosk of a Switch dominated event, even hilariously going as far as to place a Switch in Handheld mode next to the 3 current models as a "fourth" handheld option, despite Nintendo insisting the Switch isn't a successor previously. Yeah, real subtle guys.

Nintendo can say the 3DS will co-exist with the Switch all they want, but in the end, it's the consumers who'll be the judge of that. Right now sales have plummeted everywhere both in hardware and software, as more people move over to the Switch. Surprisingly however, hardware sales have still been pretty decent in North America all things considered, probably because it's so cheap along with its massive library. But that may change come Black Friday. The One-Two Punch of Pokemon Let's Go! and Super Smash Bros. Ultimate will surely have the eyeballs of gamers and parents with kids. And without a major release for this Holiday, the 3DS is going to have a tough time justifying itself in post-Switch world. I'd say we're looking at, at least one more year of first party release for the 3DS before Nintendo pulls the plug in 2020. 2019 is when the Switch will really start feeling like a Nintendo handheld as all the 3DS series such as Fire Emblem, Pokemon, Animal Crossing, and Luigi's Mansion will all have sequels on Switch that can be played on the go AND on a TV, and that's not even talking about whatever else Nintendo has lined up in 2019. 3DS will have a few more first party games, but don't expect anything cool. We'll see Mario and Luigi, Kirby, the long awaited Yokai Watch 3, and maybe another port, but everything else will be Switch and Mobile in 2019.

For as long as they want. They're selling the NES and SNES still.

3DS/2DS is perfectly suitable for kids looking to get introduced to all the main Nintendo IP. If those NES/SNES games are still fun to play today, then 3DS/DS games will be fun for years to come.

A 6 year old doesn't need a $300 game system, or even a $200 one.

It's a good kiddie platform. Nothing wrong with that, they need their first game system at some point too. There are hundreds more perfectly good DS back catalog titles they could offer on 3DS via the eShop too.

They don't even need to release new games for it, turn it into a digital platform and make all the GBA/DS/3DS games available on the eShop. Just keep selling the system. 

That's a nice short-term plan. But eventually, more kids are going to want a Switch over it, especially once Pokemon comes into the picture. Nintendo can sell the 3DS for quite a while, but eventually sales will decline even further and they'll need to retire it. 

When kids get to age 9-10 then they can move up to a Switch, I really don't see why a 5 or 6 year old needs that. The 3DS has perfectly fun versions of virtually every Nintendo IP that teach every kid all they need to know about those IP, as they get older they can "switch" up if that's what they want to do. 

But the Switch, even a die-shrunk, smaller version is probably years away from being sub $200. 

January - September 2017 3DS sold 3.6m units and 18.8m of physical software.
January - September 2018 3DS sold 2.35m units and 7m units of physical software.

It's dying, in 2019 it will probably sell 2.5m for the whole year.

I'm betting even lower than that. Last year the 3DS had a new Pokemon game to keep it afloat amidst the Switch. But with Pokemon Let's Go! and Gen 8 on Switch and no major Holiday title, I think Nintendo will miss their 4 million sales projections for the system, if only by 1 million. 

its got a great library and its a cheap handheld for what it offers.

As long as Nintendo keeps supporting it with a few decent games a year. It's very profitable, and Nintendo can eventually make it cheaper, and cheaper. With that library and price point, if they keep giving people reasons to buy in, for themselves or for their kids I can see them dragging it out until 2020, possibly even later. My guess is that they keep this alive until Switch is able to take its place when Switch 2 eventually releases.

Realistically, until the Switch drops down to a price low enough to make multiple Switch units per-household possible (around $200). I don't think that's going to happen until 2021~ish but I do expect 1st party software support to end after next year.

Until switch receive a mini version, PSVita size or smaller, (maybe even rebranded if do not make sense calling it switch anymore), in the 150$ price range or lower (sold at profit), with higher battery life.
maybe it will only be realistic in 2 or 3 years. 4 years might be the upper limit.