I once came across this quote: "Pride is a cold, stormy, barren mountain".
It seems to me that this has played out in spades at Rocky Top. Whether or not her illness was a contributing factor, it was Pat's pride, and the oversized pride of folks like Cornelius that abetted her, that played a role in the decline of the Tennessee program.
I believe that refusing to continue the series with Connecticut has contributed to their program becoming stagnated. First, as has been oft mentioned on the BY, the game has evolved over time, and much of that evolution results from Geno and staff's coaching brilliance. Until South Carolina's recent rise, they still dominated the SEC even though they didn't do well in the NCAA's - gives a false sense of strength. Had they kept the series going, and assuming they had lost, it is likely that Pat and Holly would eventually realize that they needed new offensive schemes - that the old way of relying on a dominant big to grab all those offensive rebounds just wasn't good enough anymore.
Second, top notch recruits thrive on challenges. They want to play the best their sport has to offer. For several years, that best = UConn. I have no proof but I would think that keeping UConn off their schedule has had some impact (admittedly minor) on some prospects opting for other schools. I recognize that, 2016 recruiting bust aside, they have still been getting quality players. But they are missing out generally on their really top choices. Even if current recruits don't know much about the feud, and are even perhaps ignorant of the intense rivalry from before, they most certainly realize that Tennessee is now refusing the play the best.