it will still continue,
if you start checking attendance at feb 1, and feb 28 is the last day of the month so = 28 consecutive days, then march 1 will add 1 day to your attendance so on and so forth, now it will become = 29 consecutive days,

but there is another question

i know we haven't tried this yet but what will happen to days if you choose 5 olives with 12 consecutive days, 5 olives = 10 days... i really doubt that there will be bug/error -.-