Lots of people will tell you their favorite numbers. However, the bankroll you need to be safe depends on your win rate, and we don't know what your win rate is, or even that you are a winning player.
A simple consistent guideline is
bankroll = comfort * standard deviation^2 / win rate.
You can use this formula for many different advantage gambles, such as cash games and multitable tournaments.
The standard deviation for a HU SNG is close to 1 buy-in.
Comfort depends on your personal risk aversion and your ability/willingness to move down. You can use the same comfort level when you play different types of poker. Usually a comfort level of 2 is considered aggressive and a comfort level of 4 is conservative.
For example, if you choose to use a comfort level of 3, and your ROI is 5%, this suggests that your bankroll should be about 3 * 1/ 0.05 = 60 buy-ins. If your ROI were only 2%, you would need 150 buy-ins for the same level of safety.
If your bankroll drops below the target amount, you don't have to stop playing, but you typically should not play when your bankroll is below half of the target amount, and before then it would probably make sense to play at a lower stake level.