Can a horse be entered in two races on different dates?
He is already a winner of one as he won his first race date, which makes him winner of two.
He shows up a month later entered in a new race of two.
Answer: Horses are frequently entered in more than one race, but that doesn't mean they'll run. Often they'll show on the entries list, but will be a scratch, either by the racing secretary or the trainer.
An allowance race for non winners of two races (example on the past performances Alw 90000n 1x) often have other conditions, such as "non-winners of two races, which have never won $15,000 other than maiden, claiming or starter."
That means the horse is eligible if they have won two allowance races with a combined purse money of less than $15,000. They are eligible if they have won maiden, claiming, and/or starter races.
Non winners of 1 (or 2) is an allowance race frequently used by maidens or claimers stepping up in company and the owner or trainer doesn't want to run them for a tag (claiming race).
Today's 2nd race from Saratoga (25th July 2021) illustrates this.
Note in the past performance of Our Destiny that the horse ran in an A72000n 1x twice, but didn't win.
Those were allowance races with a purse of $72,000 for non-winners of 1 race other than maiden or claiming.
Because he didn't win the allowance starts, he's eligible for today's race.