While doing things like say, punching cops, obviously raises some red flags for some character issues; there's also the other more tangible reason teams stayed away from him. It's probably the #1 reason that Dennard slipped.
The whole jail time thing.
If Dennard is convicted of third-degree assault on an officer he could be sentenced to up to five years in prison. He is also facing misdemeanor counts of assault and resisting arrest, which each come with a sentence of up to one year in prison.
By all accounts of Dennard's coaches and teammates, he seems like a good enough guy. Though obviously officer Benjamin Kopsa would take a different stance on that.
Alfonzo Dennard stepped in to shore up a leaky Patriots secondary this season as the seventh round gamble paid off. The corner was originally graded as one of the top prospects at his position in last year's draft class. With both Aqib Talib and Dennard in the secondary, the team's pass coverage improved dramatically as the team advanced to the AFC Championship game before falling to the eventual champion Baltimore Ravens.
Now the Patriots face an interesting situation. With Aqib Talib being a free-agent and Alfonzo Dennard facing up to seven years in the can, the cornerback position is - once again - a desperate area of need.