Does vision still get worse with age even after cataract surgery?

If you do not have any other eye diseases, the vision often remains clear after cataract surgery for the rest of your life. 

 

Most age related change in vision is due to the lens of the eye.  Cataract surgery replaces the lens inside the eye, so there is not further reason for your vision to deteriorate with time.

Unless you have some other eye illness or pathology like macular degeneration or glaucoma, your vision after cataract surgery should remain every good.  
Sometimes the lens implants develop some scar tissue membranes on them and need to get zapped away with a quick and painless laser procedure but this is quite common and most ophthalmologists are quite skilled at treating it.

The vision should be great or even better and perhaps with less glasses dependence after surgery.
Ask you doctor if you have any other eye condition which may diminish vision later. Macular Degeneration is perhaps the most common condition that would do so.