However my participants are reporting that after day 3 their previous responses are being displayed instead of the new day.
Sounds like you sent a reminder email (that contains the same URL like the original email) instead of a new mailing für the third day.
Please double-check the settings of the mail that has been sent on day three.
I am at a loss.
You shall always (!) do sufficient technical pretests before working with laborious designs.
Important: Please note that it is not useful to create one large survey for a diary study (see Multi-Wave Survey). If you do so (what I strongly discourage), make sure that the threshold for missing values (set in the questionnaire settings) is small enough so that the survey won't restart unintendedly.