I dug my Apple-brand lightning SD card reader out of storage, plugged it into my iPad Pro (the larger current model running iOS 11.2.5), and inserted a newly made test SD card (freshly formatted with two test JPEG pictures). The Photos app popped up in Import mode. The entirety of both pictures showed up in the thumbnails. After import, they both showed up in their entirety. Both uploaded to iCloud Photo Library and downloaded to my other devices.
Let's examine the differences between your setup and mine.
My Apple-brand lightning SD card reader (model A1441) might not be the current version. Did you buy your reader recently? What model is it? (If you didn't keep the box, the model should be in tiny print on the reader.) Have you ever used it successfully, or is this the first time you've tried it? (You might have a defective instance; it can happen.) Have you tried it on a friend's or store's iPad to see if it works correctly there?
My test SD card is only 1GB, so it's not SD-HC or SD-XC, just SD. How large and what flavor of SD is your card?
My SD card is formatted as FAT16 by my camera, reasonable because it is only 1GB. How is your card formatted?
Have you tried multiple cards to see if the error persists? Are they the same variety and formatting?
My test SD card has been used with success previously. It was taken out of service only because I got larger cards. Have you ever been able to use yours successfully?
My test pictures were taken in JPEG only at 5472 × 3648 resolution with a Canon G5 X camera. Are yours JPEG, RAW, or both? What resolution? What camera (especially if you are shooting RAW)?
My iPad Pro is the current 12.9" model running iOS 11.2.5. Is yours the same model? What software level?