Fans don't love Kelly, but they don't hate him enough to get the admin to send him packing. That's the thing about averaging pretty good seasons, with an occasional great one. Typically that's good enough.
Kelly benefited from four bad hires (only three of whom coached) before him, but the death of the video operator was a big issue, as were his tantrums, early. Playing for a national championship in year 3 helped him a lot, though getting crushed in it tempered that a bit. Curiously, I don't get the sense that the sanctions wiping out all the wins in 2012/13 did much damage to him, but maybe I just haven't been following closely enough. 2016 was bad, but a 4-win season would be bad for any coach. However, making the playoff last year bought him at least a couple more years (barring something stunning). Only four coaches have been at ND longer than Kelly, and you've heard of them: Rockne (13 seasons), Leahy (11), Parseghian (11), and Holtz (11). His .704 win percentage is behind them, Layden, and Devine.
If Kelly can get a national championship, they will make a statue of him. If not, he will be remembered as the worst of all worlds (except the Willingham and Weis worlds): good enough to keep his job, not good enough to take ND where it expects to go.
He's 57 now, going into a year ranked in the top 10, with two very tough games on the schedule (at Georgia, at Michigan), so the likelihood of another CFB playoff berth this year is low, but expectations are for a 9-to-10 win season, which is easily good enough to keep him around. That schedule also sets the Irish up for a great season, because outside of those two games, the only other ranked opponent (preseason) on the calendar is at #25 Stanford. A couple of big road wins, and the Irish could definitely be in the playoff again.
But I also think that Notre Dame's fan base is in danger of permanently lowered expectations. It's been a long time since 1988, and a lot of great coaches have done well at places other than Notre Dame. All the new alumni over the last 20+ years have only heard of ND's greatness, they haven't witnessed it. This is especially true because literally every time the Irish have been close over that time, the last game was a blowout loss:
2000 (Bob Davie's best year): blowout loss to Oregon State in the Fiesta Bowl;
2002 (Willingham's big start): blowout loss to NC State, to finish on a three-game slide;
2005 (Weis's first year, the year of the Bush Push): 14-point loss to the Buckeyes in the Fiesta (and most people remember that it felt like a blowout);
2006: blowout loss to LSU in the Sugar Bowl (immediately after a blowout loss at USC);
2013 (MNC): just a whuppin--it was probably worse than the 28-point loss looks on paper;
2018 (CFB): another beat down; at least Clemson did the same to Alabama the next week.
That's a lot of hard landings. Winning the Hawaii, Sun, Pinstripe, and Music City Bowls doesn't heal much. The Citrus over LSU was nice, but still, not close to the big games other programs are winning.