Hi,
Starting with Adobe Reader 9 > Acrobat 8 direction first. Data entered in Reader cannot be saved unless the form has been Reader Enabled beforehand. There are plenty of threads on Reader enabling forms.
With Acrobat 8 > Reader 9, I haven't come across that before. Can you open the form in LC Designer and check the binding of each field in the Object > Binding palette. It should be set to name/normal. If it is set to 'none', then this may be part of the problem.
Can you share your form? If so upload it to acrobat.com and share the published link here.
Niall
Assure Dynamics