They give 10 passes per one horse year until age 80. If they are on the exact year, and you have given care and put them to bed, the reward should've showed up on any one of the care buttons. If it's between years (Example- 45 years 4 months) You won't receive any passes until the horse hits 46 years. you need to be careful when caring for the horse on the year makers and watch which button will hand off the passes.

Hope this is somewhat helpful-Herc

this incorrect. the passes can come at anytime during the horses yr.
to answer the original question. I honestly don't know. I've never wanted to test it. one thing I definitely wouldn't test it on would be if you got it at any yr and 10 months.

I've accidentally aged past it and it never showed up again during the year. This would make sense, as passes will show up on the exact same ages if you use a piece of cloud. (Example 10 years 10 months and 11 years. If you aged back, you'd get the passes again) You can still claim the passes if the horse hasn't been aged.