Meh. I pause mine whenever I'm going to be away for more than an hour, because I can't be bothered to reset the time. Baby tamas need lots of care, and will sicken and die pretty quickly if you're not on top of things. Adults can go longer, as other people have said.
Can someone please explain to me how pausing a tamagotchi drains the battery? Whether your tama is awake, asleep, or paused, the clock runs constantly, so aren't the batteries experiencing a drain no matter what state your tamas are in?
As for pausing causing the growth of tamas, I can't say that's been my experience. I might pause for an hour or so, but when I unpause, I play with my tamas so that they get the skill points they need. As a result, my tamas generally reach full growth by age 4.