Mark Teixeira's 2015 season had people thinking that maybe the Yankees would need to find a way to bring the first baseman back after his contract expires at the end of this year. He was very productive in the heart of the lineup until a broken leg prematurely ended his season. The silver lining of that injury was that it gave Greg Bird a chance to show why he was made virtually untouchable by Brian Cashman, and the young first baseman did as well as one could hope.
Unfortunately, Bird likely won't return from his shoulder injury this season and his replacement, Dustin Ackley, is now out for the remainder of the year with a torn labrum of his own. Suddenly, the Yankees' first base picture is basically Teixeira and not much else.
The Yankees are still getting great defensive production out of Teixeira, but his offense has been downright atrocious. His 57 wRC+ on the season is down near what it was back in 2013 when he played only 15 games all year due to a wrist injury he suffered in the World Baseball Classic. Teixeira hit three home runs that year, and he has just three in 45 games so far in 2016.
Teixeira has also already missed bits of time with little nagging injuries that aren't severe enough to send him to the disabled list. Such is the life of an older player, but it puts the team in a very difficult position now that their two main backups at the position are done for the year. Austin Romine is likely the primary backup first baseman. He's hitting better than Teixeira at this point, over a more limited sample, but his defense isn't going to be anything like what Teixeira brings to the table.
Beyond Romine, the Yankees would probably need to look to Nick Swisher in Triple-A for their next first base option. Swisher got off to a pretty good start after rejoining the Yankees on a minor league deal, but those numbers dipped dramatically in May when he batted just .200/.207/.278 for the month. The Yankees may have missed out on Swisher's productiveness, through no fault of their own. Rob Refsnyder is also now taking grounders at first, but given how poorly the third base experiment seemed to go, it's tough to be too optimistic.
Obviously, the Yankees need Teixeira to turn things around at the plate as soon as possible. They also need him to find a way to stay on the field. History says the former could happen, but the latter isn't likely. Losing Teixeira for any length of time would hurt defensively right now, even if not so much offensively. Should he turn it around, though, the team would be missing a huge bat in the middle of their order that they really cannot replace.
It seems like the question of keeping Teixeira around beyond 2016 is no longer much of a concern now, especially since Bird will be back as long as his rehab goes well. The Yankees might miss Teixeira's strong defense at first, but they are already missing his bat in the lineup, even though he hasn't gone anywhere.