Offline Cards are cards that can't be checked. Something has changed with the card and Elf can no longer check your card. Cards that stop working for Elf checking are marked "Offline" in the card's "Status" field.
Cards can stop working for various reasons; they're usually fixable but require your attention. Check if any of the following applies:
Verify that your card has been updated by clicking Check my Cards.
If everything is set correctly but Check my Cards continues to show your card has a login failure, submit a bug report.
* The reasons for blocks can vary -- too many overdues, fines, card may need renewing, etc. To remove the block, you will need to get in touch with the library. (See the FAQ for more on blocks.)