In 2000, George was battling cancer and also recovering from 40 stab wounds he received from an intruder to his home. According to wikipedia, he was first diagnosed with cancer in 1997, but after a year or so of chemo & radiation was told it went into remission, but it returned.
I feel the main reason he didn't accept was due to health reasons.
Also, in my opinion, I think he was on a spiritual path where he felt those kind of awards just didn't matter much to him, and he didn't feel the same sentimentality to the crown that Paul has always had. Don't think his non-acceptance was because he was jealous of Paul, or angry that he wasn't recognized in the same way.