Years pass by in-game. As years pass by your character's age increases. If your physical age goes past your decline age you will start to lose BP as the years pass. But you are only losing AVAILABLE BP, not BASE BP. What you gain when training is Base BP, and that keeps going up. Available BP is just how much of your Base BP is currently available to you. Many things can alter that, such as powering up.
Each race has drasticly different decline ages and decline speed. You can increase your decline age by gaining energy. Most of the time you don't have to worry about dying of old age. Servers usually wipe the save files long before you reach old age.
When you die of old age your age is reset and all your power comes back to you.
Being old has advantages. Depending on how far declined you are, your bp/stat/ki/sp/skill mastery/leech gains increase. The further you get into decline the greater the increase. The increases maxes at x1.41 for all gains. You will be the ultimate sensei. The loss of available bp will overshadow your increased gains in the long run, and your students will surpass you always if you train them to completion.
When your power is declined to 50% you are receiving the maximum possible boost. You can figure out the gains increase your receiving by doing 100 divided by the % of power you have remaining, then square rooting it. So if your power is declined to 80%, you do 100/80, which is 1.25, and the square root of 1.25 is 1.12x gains. If your declined to 50%, 100/50 = 2, square root of 2 = 1.41x gains.