Some users created new items in the list, but the items didn't save at all.

DGWCYFirst of all if you could share what type of form you are using for new item creation:

Out of box, power apps or custom.

Usually if user don't have contribute permission they will never see the new button, but as they can see so they have contributor permission. Now few things can happen if there is list which expects data but not visible on the form can lead to this type of issue. Second thing can happen there are certain columns where you want some values to be unique which will prevent users from entering data if that column has any duplicate value. Finally if there are some Event handlers associated with the list which can control item creating event and not allowing for some reasons.

Try with this options you should find the root cause if all these fails then you have a bigger problem where you need MS's help to understand if there is anything going on at your environment level.

Thanks,
Vik
If this post helps, then please consider Accept it as the solution to help the other members find it more quickly.