He actually got a two year contract when he was 32 (2001), it was only from 34 onward that he got one year deals.
Wenger said: "It's not over 30, it's over 32. So when you have a player [who is] 32 he will just get a one-year contract. It depends on the positions as well. If a central defender, then no problem to sign them until 34. But a striker is different. After 32 you go from year to year. A midfielder as well, after 32 you go from year-to-year."
On 16th January 2001, he signed a two year extension, taking him to the end of the 2002/03 season, at which point he was 34. "This contract will almost certainly be the last one I ever sign which means I'll be finishing my career here at Arsenal," a delighted Bergkamp told icons.com.