Disable the disk check when reconnecting an improperly disconnected disk to OS X

Open Terminal and enter:

#Get the disk identifier of the ExFAT partition
diskutil list
#Get the UUID of the ExFAT volume with diskXsY being its disk identifier
diskutil info /dev/diskXsY
#Create and edit /etc/fstab 
sudo vifs

Add a line with the following content after activating insert mode (e.g with I)

#Replace the UUID below by the one found earlier!
UUID=2FECDB7A-15F0-36F9-9A47-483B9669D6DC none exfat rw,auto 0 0

Hit esc to leave insert mode. Enter :w! to write the file to disk and :q to quit vifs.

Reboot your Mac.

The last 0 should disable fsck.

An alternative method may be: rename /sbin/fsck_exfat to /sbin/fsck_exfat.paralyzed with:

sudo mv /sbin/fsck_exfat /sbin/fsck_exfat.paralyzed

Since /sbin/fsck_exfat is a link only you may also have to rename the original file: /System/Library/Filesystems/exfat.fs/Contents/Resources/fsck_exfat.

Both methods are not recommended! Instead the USB socket should be repaired.