Every character has "power boost" levels, in which his or her stats (such as HP or Agility) raise dramatically (sometimes 20 or more!) To ensure the highest attributes for each character, save the game before a character raises to a "power boost" level. Because the numbers his/her attributes increase by are random, reset the game if you aren't happy with the new statistics.
Here is a list of the "power boost" levels for each character.

Rolf: every 4 levels
Nei: every 8 levels
Rudo: every 3 levels
Amy: every 6 levels
Hugh: every 6 levels
Anna: every 8 levels
Kain: every 7 levels
Shir: every 6 levels