Time to change trains in Palencia

Not so long ago, trains in Spain used to run on time, but since foreign companies have started operating on the Spanish rail network and since speed restrictions have had to be introduced due to  maintenance, everything has been delayed…

In my opinion, 17 minutes should be enough time (it might be the second train that’s delayed). If the first train is delayed and you have a connection, get in touch with Renfe staff; they always try to find a solution.
As for security checks, they’re usually quick and, to be honest, they’re well timed to coincide with the train’s arrival. I’d recommend checking the official Renfe website to see which items are prohibited, because, for example, if you’re carrying scissors or a pocket knife, for example, they’ll make you throw them away. 

I've taken this route two weeks ago and had a delay of half an hour between Valladolid and Burgos due to temporary speed restrictions: there are various single track sections due to works, so delays are likely (there is only competition from freight carriers on this route).

Officially, Renfe only guarantees onward connections if there is at least 60 minutes between trains (90 if between different stations in the same municipality). So if you miss it, you'll likely have to arrange yourself. You might be able to claim compensation from Eurail.

Be aware there are engineering works currently affecting the MD entry into Palencia (not sure how that'll be in July): The arrival at 16:08 is by bus from Venta de Baños. Renfe hasn't published timetables for July yet.

If you want to go by train, consider taking an Alvia (or the MD) from San Sebastián to Valladolid and switch there to the AVE/Alvia towards Oviedo. 

If the train and connecting train replacement bus would be punctual, 17 minutes is plenty to make the connection: Palencia is a small station with just two platforms, and security checks are quick if necessary (only on one of the two platforms). As 29 July can be a busy travel day, consider booking reservations on both as a backup.