There are nearly 3 million google hits and 2 million yahoo hits for CON'T as the abbreviation for continue/continued.
It's not a form listed in popular dictionaries.
cont.
contd
cont'd
cnt
Why do you suppose it has become so common?
Perhaps:
- It's an abbreviation of an existing abbreviation: cont'd / con't
- The apostrophe is a stress mark for the pronunciation of the word instead of replacing letters
- Abbreviations can have slang forms too