I firmly believe that by the time E3 2019 rolls around, Nintendo will come out and say the 3DS is being discontinued. Already there is enough evidence regarding Nintendo's behavior that points to them being ready to retire the console. 

The first major point is the life span of Nintendo's other handhelds, which accounting for mid-generation refreshes, gives each console a 3-44 year lifespan. The DS was released in 2004, then the DSi in 2008, the 3DS in 2011, and the N3DS in 2015. By E3 2019 the New 3DS will be over 4 years old in all regions, making it a good time for a new handheld, or just discontinuing the line, which is the route i think they will take.

Not only that but Nintendo is demonstrating a lot of the same behaviors that they usually show when a console is nearing the end of its lifespan. They outright said that they have plans to continue supporting the 3DS is 2019 alongside the Switch, but this doesnt mean much since they say this all the time and never live up to it. They said the GBA would receive support after the DS was released, which it didnt. they also said the Wii U would still receive support after the Switch released, which it didnt. So why should now be any different? 

Even considering how the audience reacts to 3DS game announcements is a big red flag for the console. People simply do not want to spend more money on 3DS games, myself included, and I know far too many people who feel the same. The switch has redefined handheld consoles, so seeing dedicated handheld games feels like a missed opportunity, like the games could have been better if they were made for the Switch. Even GameFreak is jumping ship by now making the Switch the new home for Pokemon game releases. so in the scenario where Nintendo doesnt abandon the 3DS and/or makes another handheld console, it will be Nintendo's first handheld EVER to not have a pokemon game. the games which move more software sales than any other on Nintendo's handhelds, would not be there. 

so im firmly stapling my prediction in now. By 2019 Nintendo will formally announce the 3DS is discontinued

Nintendo already has 1st party titles announced for 3DS in 2019, how are they going to expect to sell Mario & Luigi: Bowser’s Inside Story + Bowser Jr.’s Journey if they don't even make or sell the system anymore.

2020 seems more likely in my opinion, they have 3DS already foretasted to sell a certain target until March 31st 2019 and I don't seem them discontinuing it just 2 months later in June 2019 when Nintendo themselves have promised new 3DS games will be coming "in 2019 and beyond". http://www.ign.com/articles/2018/04/27/nintendo-promises-support-for-the-3ds-through-2019-and-beyond

If Nintendo can sell 360,000 units of a nearly dead handheld in the slowest quarter of the year, production is not going to be discontinued soon. You won't see more games after 2019, but the system will be produced as long as a non-trivial number of handhelds are sold.

Only way I see it happening by then is a smaller handheld only Switch launching with Gen 8 Pokemon.

I can't see that happening at all

It'll more likely be discontinued 2020 as that would be the point Pokemon has fully settled on Switch and AC will likely be on the way, 3DS still has releases for next year.

Agreed, with 4m hardware for this fiscal year thats too much to just call it quits even if the miss their forcast.

They didnt stop shipping DS until annual shipments were down to 130k and Wii when it was 110k.

3DS has at least one more fiscal year before getting discontinued.

Me too, albeit I see it more likely to be discontinued in the second half of 2020 ( if not 2021 ) , in the end of it, one last holiday.

Nintendo also even bothered to ship 40k gba units in first calendar quarter of 2009.

Depends on where hardware sales are by that time. I don't think Nintendo would like to sacrifice 4M+3DS units like they're selling now per year. I think it'll be discontinued in 2020 or early 2021. Then they'd ding it down to like 70 bucks for a New 2DS XL and sell another crap ton. When it's all said and done, it's going to be in production/supported for a bit more, and it'll hit 80 million.

You don't discontinue something when you are seeing growth, currently Nintendo is seeing growth in 3DS hardware. Makes no sense to discontinue it so early.

I'd say 2020 is more likely. Simply because by that point, Nintendo will have taken the Switch as far as they want to. People are already using it both at home and on the go just like Nintendo envisioned it, they're looking to sell the Switch to one per-person and are already on track to do so, and many of the 3DS' best IP will have migrated over. Plus, Smartphone games will have been more successful for Nintendo, and the Switch would already have a price cut under its belt. 2020 is when the 3DS will officially die because there would just be no incentive to keep it around for much longer. Sales are already way down this year, with no Pokemon keeping it afloat, it's going to get slaughtered this holiday onward.