The problem may be with that segment you want to travel from La Coruña to Segovia. Trains in the northern region of Spain are not as prompt and advanced as in some southern segments. We tried booking from Santiago de Compostela to Salamanca and it was not as easy as the other train segments we booked. For instance it takes 6 hrs to travel from Sto. de Compostela to Salamanca (198 miles) when the fast train from Madrid to Sevilla (250 miles) takes only 2.5 hrs. We ended up deciding to rent a car and drive most of the north coast because we had the time to do it. If you don't, I've heard there are good bus services also. Another thing you may want to try is calling one of the train re-selers (Rail Europe,Eurail) and asking questions about that segment, you don't have to buy anything from them, but at least you'll have another opinion on what's going on with RENFE.

changes schedules usually its the summer july, then strikes are always a concern, but from many forums the RENFE site is special, time and try again.

In my perusal of Renfe, I have noticed that Sundays do not seem to offer any special fares. Is this the norm? As I'm looking, I can find special fares during the week, but Sunday is full price. It is a big enough difference to make me change my travel plans. Can anyone confirm that Sunday travel on Renfe does not typically offer a web discount? (When I traveled last year on Easter Sunday, there were no specials, but I figured that was because it was a holiday)