If answers are not being saved on a Form, it is likely an issue with the position of the Question(s) in the Online Form Sequence (Plan > Select your Form > Setup > Page Setup).
When Questions are displayed before the Registrant Details page in the Online Form Sequence, answers will not be saved because there is not yet a Profile designated to assign to the answers. The Registrant Details should be collected first before asking any Question on the Form. This way, the answers will be assigned to a Profile.
One exception is if the Profiles are imported/uploaded to the Event, and the Entry page is collecting a username/password. In this case, a Question section can be placed before the Registrant Details page because a Profile is already created on the Entry page, and the answers can be assigned accordingly.