for insufficient material it does. For threefold repetition, you have to press the "offer draw" button to claim a draw when a position has repeated itself 3 times. For a perpetual that is not a threefold, you have to take the time to keep checking until it is either a threefold, in which case you claim the draw, or 50 moves, in which case you also claim the draw.
Drawn Games
If you need help, please contact our Help and Support team.
Why does Chess.com not declare a draw game in the case of Perpetual Check, or of Insufficient Material ?