I'm genuinely quite torn on Jagielka. Although much of what
@davek says can come across as a little full on I wouldn't easily discount all of it, I think there may well be a basis for it.
That being said experienced players are important for any business, particularly if they are on side and behind the manager. It certainly appears that Silva respects the role Jagielka has and Jagielka seems relatively content in the squad role.
You also have to factor in, if Zouma goes and Mina/Keane are back late from international duty we are going to be quite hard pressed for centre backs early into pre-season. The likelihood is we may need 2 cbs and the feeling may be, when you factor in transfer costs, agents fees etc that it is just cheaper/easier to keep him on another year and hopefully allow Gibson (and to an extent possibly Feeney/Holgate) to develop.
You are spot on about how his seasons go too. The last 2-3 it's the same pattern, he really struggles at the start but comes into his own at the end. His performance in last seasons Godsons derby was one of the best defensive displays I've seen in a derby. He just hammered everything clear.
To me he struggles to get the pace of the league early on. This is pretty natural for a lad of his age, it's just too quick and it will take him longer to get fully match fit. I also think the league pace slows down in the 2nd half of the season, it is less ferocious and sides begin to pitch in for draws more often and this helps him.
It's difficult to know what to do as in truth its dependent on a lot of other questions. How much money is available this summer? What other areas does the manager want players? What are they doing with Zouma? Has Mina settled? Is The interest in Keane real? How do they feel about Gibson, Holgate & Feeney? etc