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.

After cataract surgery the vision should be clear. The weeks after the surgery can result in blurred vision due to uveitis or macular oedema particularly in diabetic and those with darker eyes. In the months and years after the surgery the vision can change due to a condition called posterior capsular opacification which may require a simple laser procedure. The cornea which is the front surface of the eye can change in astigmatism over time meaning you need a change in glasses to keep the vision clear.

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.