You need to do some basic troubleshooting:
Try a different card, maybe a non-Eye-Fi card, to see if it is the card or something else.
Try a different method for transferring the photos to the computer, perhaps without using the Wi-Fi capabilities, to see if the photos are on the card ok.
When you have a few bad files in a batch, try copying those photos from the card to a temporary location on the computer's internal hard-drive, a second or third time, without using LR or Wi-Fi, using just the OS functions, Explorer or Finder, then import them into LR from that temporary location.
About the only way it could be LR is if the camera is writing the data onto the card in an unexpected way, that LR hasn't been programmed to recognize, an EOF error is the typical issue, but that isn't specific to Eye-Fi or a card type or brand.
Typically, the next shoot I did produced no import errors! However, if and when the problem arises again, I shall go through the steps suggested and let you know.
Been working relatively OK of late, but the in the last batch I lost a good third of my shots. Same error occurs whether downloaded from the EYEFI cloud, imported directly from the camera via USB or copied in from a third party location. Getting very frustrating as Eye-Fi support say Lightroom is thiurd party software and it's not their problem, and Lightroom say it is the way the camera is writing to the card. Going back to a regular non-wifi card seems th eonly option.