"It's been really hard to play golf lately, this year. It's been very, very emotional," Day said.
Day's agent Bud Martin said Day "hopes" to play in the Masters at Augusta next month but could not confirm he would tee it up at the year's first major.
"The Masters ... I know it's something that he wants to do but she [Dening] comes first," said Martin.
Dustin Johnson had no trouble in his debut as the No1 seed. He had five birdies in his opening eight holes and there wasn't much Webb Simpson could do, but try to extend the match as long as he could. It lasted 15 holes in a 5-and-3 victory.
Rory McIlroy (No2) and Jordan Spieth (No5) face critical matches the rest of the way.
McIlroy, the 2015 champion and a semifinalist last year, appeared to seize control against Soren Kjeldsen when he won three straight holes, but Kjeldsen ran off four straight birdies to end the match. Kjeldsen was 6 under on the round.
It was the first time McIlroy had lost his opening match since 2013 when Match Play was single elimination.
"If I had played anyone else, I might have won," McIlroy said. "Overall, I can't be too disappointed. But at the same time, when standing on the 14th tee just having won three holes in a row, I thought I had him going into a tough stretch of the golf course. But he put up three birdies in a row, and you can't do anything about that."
Spieth didn't put much of a fight against Hideto Tanihara of Japan, making his debut in Match Play.
Spieth and McIlroy are not done yet, though they need some help.
The best record from the 16 four-man groups advance to the knockout stage on Sunday.