Harry divorced with his wife, Debbie, after the second season after he lost his job as principal of West Beverly High School. His last appearance was in the Season 2 final 2x22 "Confessions". It is speculated that he had enough of the drama with his wife and children that had led to his downfall. Since moving out of his mother, Tabatha's house at the end of Season 1 and into a house of his own in Season 2, there have been problems in Harry and Debbie's marriage from the very start of the second season.
Upon a second viewing of Season 2, it is not hard to see the reason why Harry left his wife and family. Harry clearly blames Debbie for her angry and jealousy over his past history with Naomi Clark's mother as well as disagreements on how to raise their daughter and adopted son. Also in Season 2, Debbie had literally spent nearly all of the family's life savings on expensive yoga classes and expensive shopping sprees as an outlet to deal with her own stress, not to mention her lack of employment which did more harm then good for the family.
Harry also blames Dixon and his gambling addiction for making him lose his job when Harry made the mistake of covering up Dixon's school break-in. Harry also blames Annie and her legal troubles stemming from her hit-and-run accident at the end of Season 1 which led to a further drain on his finances. After Annie confessed to her parents in the final scene at the end of Season 2 about her hit-and-run drunk-driving accident the previous year, that may have been the last straw for him. And also when he found out that Dixon had sneaked away to Australia for the summer after being grounded, that may have painted Annie and Dixon in a further negative light to Harry who now looked upon them as soon-to-be-adult criminals.
In Season 3, Harry is mentioned as Annie and Dixon go visit him only to find his girlfriend answer the door. Since then, Harry was said to have married his new girlfriend and moved to a hippie commune somewhere in the USA southwest to get away from modern life and its dramas. From that point, he no longer keeps in touch with his family, and neither Annie or Dixon, or even his ex-wife Debbie ever bother to see him or even mention his name for the rest of Seasons 3, 4 and 5. They act and talk as if Harry never existed, as evident when Debbie visits Annie and Dixon in the Season 5 opener "Till Death Do Us Part" 5x1. In some episodes of Season 4 and 5 when there are glimpses of family photographs of the Wilson family making up of Annie and Dixon as well as Debbie, Harry's image is curiously absent from all photos. Harry had been airbrushed out... as if he never existed.
The real reason for Harry never being seen again after the second season is that actor Rob Estes quit the series at the end of Season 2. He decided not to renew his contract for another season. He said in a press statement regarding his exit prior to the Season 2 final: "This is my final season on '90210' and I wish the show, cast and crew nothing but the best. Unlike my character of Harry, I do not have any ill-will towards the series or it's characters. I am quitting because I am looking forward to spending more time with my kids and then exploring other opportunities."