How long does anaesthetic last for?

Generally an Anethesiologist gives an anesthetic for a bit longer than the operation takes. They can't overdue it because there can be complications. If pain is expected, after which it usually is then it is given in an intravenious drip or pill form. Age is included in the formula but weight is a bigger factor. An exact time can't be determined because there are too many variables to consider. If problems are expected the patient is sent to the intensive care unit where he/she is closely watched.

The beauty of a story is that you can decide. It would be most believable for the readers if it is only one shot to be 4 hours or less. Unless you have your character have a complication or reaction to the medication. You don't have to be exact if it's within what your readers will "buy." If you knock the character out for days on one shot -- they won't buy that at all.

It depends so much on what the anesthetic is. If it important for the story, find out how long each one lasts and then use it.