Is something that happens to 2-5 teams each year very rare? That actually seems startlingly common to me given the small group of teams you're talking about.It is very rare for a team to be in both the Top 40 NET (previously RPI) and Top 40 Kenpom and not make the Tournament. Only ~2-5 teams each year fall into that category and they are typically at the tail end of conferences that already got a large number of teams in and it's the teams that racked up too many losses and not enough BIG wins despite the metrics overall liking them.
If Illinois can get 3 wins against Nebraska and Northwestern and finish ~10/10 in conference play it should be enough to make the tournament without too much worrying. 11 wins should remove all doubt even if we drop 1 game to Nebraska/Northwestern (since it would mean 1 more good win).