Live? I like to always top off to at least 100bb, our preferred games are $.5/1 $100-300, so I'm rarely close to 100bb and will often top off to $300.
In casinos if playing a 1/2 or 1/3 100bb max I'll top off to 100bb any time i dip below probably 80bb, if a $1/3 match the stack game I'll usually buy in for $300-500 and top off when I drop under $250.
I wait until I'm out of chips to rebuy. I'll usually find a spot to get my chips in at least by the time I'm down to around 20bb - but I'm almost always going to try to double up (and double up again and again if necessary) before I pay for another chip. The only exception is that if somebody who I know to be an idiot fish sits down at the table (or somebody already there confirms my idiot-suspicions) I'll buy up to their stack - I want an equal shot at all their chips.
In my home game I’ll usually reload if I drop below $100 ($1/2 $300 max to start).
At the casino I always have chips in my pocket/bag so I will add to my stack as needed if I feel it smart to do. Sometimes I prefer to have a short stack that is easy to shove all-in with if people are playing crazy.
In a live homegame... If my stack gets lower than half of a typical large pot... I feel the need to rebuy. I'm not going to bother the host to top me up for $20 ($100 buy-in), but if I drop to about $30, I'm ready for a rebuy. Playing with $30 still allows me to setmine on a typical PF raise.
Playing short stacked in an otherwise deep stacked game just limits your options.
My game is 25c/50c NLHE. It plays bigger. We buy-in 200bb deep. So an answer of 60bb doesn't really tell the story.
Personally, I rebuy when I am at 20BB - being too short stacked can hurt you.
In my home games, rebuys are allowed at any time. Max buy in is 100BB and no cash transaction can let a stack exceed this. I know a lot of people here like to allow rebuys to a percentage of the big stack, but I think the big stack got to where they are through good play and is entitled to have that advantage.
I think this is a good general rule. The question is how far below do you get before this disadvantage is significant, or in the case of live play, worth disturbing the bank. (Online, most sites have the "auto-top off feature" and it requires no effort.)
My house rule is that add-ons must be at least the minimum buy in for the game (generally 20x BB) and only of amounts that do not put the players stack over the table max (usually 100-150x BB).
So if we play 0.50 BB with a 60 max, the min buy in is 10 (The minimum is usually set at 20x BB) so add-ons are only permitted when players are at or below 50. When we play 1 BB with 150 max, the min buy is 20 and add-ons are only permitted when a player is below 130.
I do think position factors into the decision too. Being out of position is obviously disadvantageous, having a short stack in EP or blind positions in some cases may mitigate those disadvantages (having a good stack size to shove over a raise, for example), so it may be worth putting off the add on a few hands until you hold the button, but make sure to add on when you get the button to take full advantage of the best position, of course.