You will find that you have to take the second day off, since you can’t play the same letter as day one, but you also can’t play another card for the first time. At the very end of the game, when you only have one card to play, you must again take a day off, since it will either be following the 6th playing of the same letter, or the 7th playing of a different letter. However these are the only days off you will need to take, and so you can play all 98 cards in 100 days.

For example (underscore denotes a day off, spaces are inserted for readability):

A_AB ABC ABCD ABCDE ABCDEF ABCDEFG BCDEFGH CDEFGHI DEFGHIJ EFGHIJK FGHIJKL GHIJKLM HIJKLMN IJKLMN JKLMN KLMN LMN MN_N