There has been exactly 1 of those where he threw multiple picks or even a single pick in the 4th quarter. I guess that's "plenty of times" to you.
Romo hasn't lost to the Giants since 2012.
Maybe I should expand my definition some to not just be Week 17 games when I say "win or go home".
2006 Week 16 against Philly - 23-7 loss, Romo 14/29 for 142 yards, 1 TD 2 Int
(A win in that game would have won them the division, instead thankfully the NFC was shit and they got a wild card at 9-7, only to lose to Seattle in one and done fashion after Romo only managed 189 yards passing)
2007 Divisional Playoff Round - 21-17 loss to the Giants and eventual Super Bowl MVP Eli Manning (again one and done), Romo only managed to complete 50% of his passes in the game 18/36 for 201 yards, 1 TD 1 Int
2008 Week 17 - 44-6 loss to the Eagles (giving Eagles the 2nd wild card over the 'boys), Romo 21/39 for 183, 0 TD 1 Int
2009 he actually won 2 big games, first Week 17 to clinch the division and send Eagles to a wild card, then on Wild Card Weekend. Of course, come the Divisional Round they got smoked 34-3 by the Vikings where he was again held under 200 yards passing with 0 TD's and 1 Int.
2011 Week 17 - 31-14 thrashing by Eli and the Giants which clinched the division for New York and would send eventual Super Bowl MVP (for the 2nd time) Eli Manning on his way to beating Tom Brady for his 2nd ring. Eli rang up 346 yards and 3 TD's with 0 picks, while Romo managed 289 yards with 2 TD's and 1nt...although all of Dallas' scoring occurred in semi garbage time in the 2nd half after being down 21-0 at halftime.
2012 Week 17 - 28-18 loss to the Redskins in yet another winner take all "NFC East Championship Game", Good old clutch Tony Romo did throw 2 TD's, but toss 3 picks as well.
Have to say, Romo managed to check all the boxes. I know you limited your range to multiple picks or picks in the 4th quarter, but a lot of these games were over well before than. Romo managed to lose a Week 17 game that would have clinched a playoff spot to all 3 of the other NFC East teams, another Week 16 game against Philly that relegated them to a wild card instead of having a home game as division champion, and another loss to Eli in the playoffs. Interesting that both of Eli's rings have included a victory over Romo as well to eliminate the Cowboys.
So yeah, I have more faith in Eli.