Check out the Mamedev.org FAQ
http://wiki.mamedev.org/index.php/FAQ:Games for Hyper Sports and Track & Field. Under Game specific settings and information. Plenty of other games in there with specific setup needed also so worth checking the full FAQ.
The solutions the same for both - I believe some records can't save as they are zero and therefore impossible to beat and it won't ever show your best. In your case, I don't expect you can run 100m in under zero seconds however fast you bash the buttons :-)
It tells you how to set/reset them on first running of each ROM. It only needs to be done once on the startup first time and then the default (or your records, if better) will be saved ongoing.
Hyper Sports
To have the high score table properly initialized, the first time you run the game you should go into the dip switch menu, set World Records to 'Erase on Reset', reset the game F3 and then set the dip switch back to 'Don't Erase'.
Track & Field
To have the high score table properly initialized, the first time you run the game you should go into the dip switch menu, set World Records to 'Erase on Reset', reset the game F3 and then set the dip switch back to 'Don't Erase'.