There is no specific rule for jockeys in this race c/w any other race for Conditionals.
The racecard for last seasons race conditions mentions being eligible under rule (d)27. Looking up online rules for conditionals isn't giving full clarity.
However I have seen mention of being a conditional until 75 winners OR until 75 wins within last six months?
If you have a favourite Conditional from the British and Irish links in the thread today, maybe check in the Racing Post if they have more than 75 winners.
I've never heard of a top Conditional or Apprentice (Flat racing) being stopped from winning the title because they won too many races that year. So maybe you are a Conditional for a full season unless you win more than 75 races in that season.