Disclaimer - I do not "know" if this will solve your issue.  And I don't know
for sure that it will be safe. (I'm rather a newbie)
I "think" the issue is that you need to change the settings in on the table
as well as the form.
e.g:
Select "Tables" and choose the table the form is based on and open it.
When the table is open look at it in "Design View"
Select the field that you want to be "required" and in the "Field
Properties" change the "Required" option from "No" to "Yes".
It won't go into effect  until you save the table.
---! WARNING !---
Do not take this next step unless you have backed up your DB. (I had to
input a whole load of data again!)
There will be a message box that reads:
"Data integrity rules have changed; existing data may not be valid for the
new rules.
This process may take a long time. Do you want the existing data to be
tested with the new rules?"

You may get a message telling you that your data needs to be changed.
If not then it certainly will require the field wether data is input on a
form or in a table.

I am not sure if this will solve your problem but it worked for me on more
than one occassion.