We sincerely apologize for the connection problems in the Nintendo eShop. We understand this is taking longer than expected, but we can assure you that providing a solution is our top priority. We are determined to make sure everyone can enjoy all that Wii U and Nintendo 3DS have to offer. In an effort to manage the high volume of traffic and ultimately improve your experience, we are temporarily taking the Nintendo eShop services offline between the hours of 4 p.m. - 4 a.m. ET. Thank you so much for your continued patience. We will keep you updated.
Nintendo of Europe tweeted a similar statement, saying they would disable access to the eShop between the hours of 10 p.m. and 10 a.m. CET. The same goes for Nintendo of Japan, who are limiting eShop access between 6 am and 6 pm, as translated by @Cheesemeister3k. The recently-released Pokémon Bank and Poké Transporter applications have been pulled by NOJ from the 3DS eShop to lighten server load, while the North American launch has been postponed.
Nintendo of America acknowledged server issues with their digital marketplace on December 25th, Christmas day. For those who received an eShop gift card or a Nintendo hardware/digital game bundle like the Wii U-themed "The Legend of Zelda: Wind Waker HD" bundle for Christmas, these server problems are making it difficult for them to claim or spend their holiday gifts. As mentioned by Kotaku, Sony and Valve experienced similar server difficulties with their online stores, but have since been resolved. It's unknown if Nintendo will compensate users in any way for the current server failure.