Hey scottyboy, Welcome to the Forum.
I checked
Carl's Gardening Guide, and didn't see your question directly addressed, but you are not to blame for your plants eventually growing old and dying.
The only plant I've
not seen die off (when properly tended) is the Money Tree ... but I can't say they never die, just that I've always tended mine and not
seen one die of "plant old age." I'm sure if you didn't water it / weed it, it'd eventually shrivel up.
As MasterSiwel said, if you've a Sim with the "Green Thumb" trait, they can "revive" a dead plant, but even if it's "resurrected," the plant will die again (eventually).
Hope this helps, and welcome to the Forum!
-- Happytime