However, he was diagnosed with cancer shortly after entering Parliament. He recovered following surgery but again had to take a break of several weeks last year after a lung collapsed.
More recently, in spite of a dramatic change in his appearance including a marked pallor and the loss of his hair in the last few weeks, he has refused to discuss his health issues.
It is understood he met party president Peter Goodfellow and other National officials on Sunday evening to discuss his ability to contest the election and serve a third term.
Mr Peachey said his subsequent decision to stand aside was his alone.
Prime Minister John Key said there had been no pressure from party hierarchy.
"I spoke to him yesterday [Monday]. He informed me last night of the final decision he'd made. I think he's been weighing up a difficult decision for him. Obviously he's battling a few health issues. We're very sad to be losing him. We obviously wish him a speedy recovery."
Act's parliamentary leader, John Boscawen, also paid tribute to Mr Peachey, saying he and his colleagues had enjoyed working with the Tamaki MP, "one of NZ's leading educators" before he entered Parliament.
"He worked hard for his students and he worked hard for the people of Tamaki. We in the Act Party wish him well for his treatment and recovery."
Meanwhile, Mr Goodfellow said National would conduct a shortened candidate selection process in Tamaki.
Nominations open today and close on October 14. A final selection is expected around October 25.
Tamaki, for many years held by former National Party Prime Minister Sir Robert Muldoon and by Clem Simich before Mr Peachey, is likely to be keenly contested. Mr Peachey holds the seat with a 17,020-vote majority.
Speaking before Mr Peachey announced he would stand aside, Auckland councillor Cameron Brewer said he would consider seeking the nomination if the opportunity arose.
"I would be silly not to consider it as there have been only three MPs representing Tamaki in 51 years. It is a prize National Party seat."
Former city councillor Aaron Bhatnagar, who is on the Tamaki electorate committee and has previously been tipped as possible successor to Mr Peachey, yesterday said he had yet to decide whether to seek the candidacy.
"I don't think it's appropriate for anyone to be making comments on the day that should really be about reflecting on Allan's career."