Is it acceptable to place porcelain veneers below the gingival margin and on the roots?

It is best to place the veneers at the gum line or slightly above the gum line. Gum irritation could be the result of overhang margins ( your veneers not fitting exactly to the tooth) open margins, excess cement (bonding material) or violation of biologic width ( the tooth being prepared too close to your bone).It is best to have proper xrays and examination, and see a Periodontist to help you further. If too much tooth structure has been removed for the purpose of putting your teeth in line, that can irritate the nerve, an in that case you probably needed orthodontics or porcelain crowns, also if you had caries before your veneers, that was proximal to your nerve that can be the reason for possible root canal. Ask your treating dentist to explain this and possibly see a specialist. Best of luck!Dr Anthony Mobasser

That has to be frustrating!  The problem probably isn't that the veneers are on the root surface and in many cases, there is no issue with them being finished below the gum tissue.  However, in order for them to remain healthy and comfortable, certain things much exist...  The most likely issue will be one of two problems.  Ons is there is a principle called biologic width and that is related to the distance from the veneer margin to the top of the bone under the gums.  In order for the gums to stay comfortable and healthy, that needs to be about 2.75 - 3mm at a minimum.  If not, the gum tissue stays irritated and swollen.  The other big factor will be a smooth finish line on those veneers with no residual cement.  If the veneer margins aren't flush and smooth with the tooth or if there is bonding resin stuck below the gum tissue, that will great very uncomfortable gums.  
The reality is that one of the great things about bonded porcelain like veneers is that you have fewer reasons to prepare below the gum line in the first place.  It is probably not a pulp issue and it sounds from your description like a gum tissue reaction - and if that is indeed what is going on, root canals aren't likely to help.  An x-ray would help to see if there is poor marginal fit or residual cement.  It would be smart to have a second opinion and have another dentist take a look too...