The eShop isn't going anywhere anytime soon, because it's a direct source of money. After all, the Wii Shop Channel is still around.
I should note that the end of the Wii U and the 3DS are closely following the same timelines for the ends of the GBA, DS, GameCube, and Wii:
- A Zelda release at or just before the release of the successor console:
- Twilight Princess on the GameCube (simultaneous release with successor console)
- Skyward Sword on the Wii
- Breath of the Wild on the Wii U (simultaneous release with successor console)
- A Pokémon remake released just before or just after the release of the successor handheld:
- Pokémon Emerald on the GBA (just before release of successor handheld)
- Pokémon BW2 on the DS (after release of successor handheld)
- Pokémon Ultra Sun and Ultra Moon on the 3DS (after release of successor handheld)
- New models released just before or just after the successor in order to get rid of spare parts:
- Game Boy Advance SP released just before successor
- Game Boy Micro released just after successor
- N2DS released just after successor
- Wii Family Edition released just before successor
- Wii Mini released just after successor
Nintendo WFC for the DS and the Wii was discontinued on May 20, 2014:
- About 8.5 years after the service started on the Nintendo DS.
- About 7.5 years after the service started on the Wii.
- About 3.2 years after the release of the 3DS.
- About 1.5 years after the release of the Wii U.
Hypothetical dates:
- About 8.5 years after NN service started on the 3DS: July, 2020
- About 7.5 years after the NN service started on the Wii U: May, 2020
- About 3.2 years after the release of the Switch: May, 2020
- About 1.5 years after the release of the Switch: September, 2018
That puts the likely end times at either 2018 or 2020. Considering the Switch's likely role as a 3DS successor as well as a Wii U successor, and the shifting model to a paid subscription service on the Switch, I suspect 2018 is when NN will be shut down.