There are two items found in the game that will increase your monster's life span. the first is the PLANT EGG, found in the jungle expedition, which increases your life span by 1-2 years.
The second item is the GOLDEN PEACH, but can only be found every 10 years, which increases your life span by anywhere from 1-5 years depending on your monster type and how well you've bred him. It is found in the desert. I found it in in the heart of the city. It's in the the building to the right. SUGGESTION: Get a class C, intelligent, part Gali monster, and freeze it. Take it out on October 1. Karn comes the next week. Put it back when you're done.
Using a lot of pills/vitamins will cut your monster's life span by anywhere from 1-5 years. The better you treat your monster (give him meat the month of his birthday along with an apple cake, after you win a tourney, etc.) will increase his life span as well. If you combine 2 monsters who have been loaded up on drugs, your new monster will only live about 60-75% of the time he normally would. During your monster's first couple of years, you should only punish him every 3rd time he messes up. After his first couple of years, he should mess up only rarely.