Probably because you are using a product that has not been supported for 10 years (9.3.1) and the extensions have been updated make better use of the processioning capabilities of the more updated software.
You may need to simply upgrade to 10.7
I would suspect that there's been an operating system update or other software update sometime since last year that may be interfering with the software. What operating system are you using?
Does ArcMap and ArcCatalog work? Are the extensions turned on? What error message do you get when you attempt to use one of the extensions?
My operating system on my portable is Win 10. and on my legacy system it is XPsp3. ArcMAP 9.3.1 and ArcCatalogoperate on both, but the permanent extensions do not. On both, I get a message that " you do not have the necessary license to execute the selected tool [3dAnalyst]".
Upgrading to version 10 is problematic since I am retired and do no have the funds.
Just to confirm, are the extensions turned on in the software itself?
In 9.3.1, select Tools > Extensions > check on licensed extensions
Melita