Causes of VVT not working?

No. You will likely lose some maximum performance but you are unlikely to notice it in 'normal' driving.

Did you test it correctly? (Remove wires and put 12v to terminals.......hold them there a few seconds and engine will run very lumpy, almost conk out)
Does the solenoid at least click? (Might just be the solenoid?)
If solenoid clicks but engine doesn't go lumpy, then likely an oilway problem (of course a visual test that the plunger is going in-and-out and is contacting the pin is necessary)
Somebody been in the cam cover recently and forgot to put the plunger back in, or worse, the plunger fell into the engine when putting the cam cover back on!?

Mike in Canada wrote an excellent thread on getting his VVT working again......and certainly noticed a difference between a working VVT and not.
Like Eric says it won't harm the engine, but the VVT does make some overall performance difference.

http://www.alfabb.com/bb/forums/spider-1966-up/309313-how-do-you-test-vvt-mechanicals.html

I assume you are saying that when you floor the throttle, the vvt solenoid isn't activating?
If so, pop the harness off the solenoid and apply a 9v battery to the terminals (polarity is not important).
It it now activates, your problem is either the inline fuse on the passenger fender wall or the throttle position sensor. Test those to find the culprit.
If it doesn't activate, remove the solenoid and take the plastic cover off the end and clean the assembly.
Put the assembly back together and test it again with the 9v battery. If it still doesn't work, you need a new solenoid.

You can refer to this post for this.
http://www.alfabb.com/bb/forums/spider-1966-up/415594-vvt-solenoid-really-dead.html

Otherwise the post SS4 attached the link for if the solenoid activates, put the mechanical portion of the vvt doesn't appear to be working.

mcola said:

It it now activates, your problem is either the inline fuse on the passenger fender wall or the throttle position sensor. Test those to find the culprit.

Click to expand...

There's actually a third possibility. It could be a bad circuit board within the connector that attaches to the solenoid. If that's it, you will either need to find a used replacement harness, or come up with another solution. My improvised solution is in the attached link:

http://www.alfabb.com/bb/forums/spider-1966-up/361529-replacement-electronic-vvt-harness.html

You'll get better advice on fixing it if you list the year of your car. The solenoid actuation is different for the S3 and the S4 models.