The answer to this isn't always strictly an issue of time, if the question concerns abandonment of permanent residence. Speak to a lawyer about how best to deal with this in light of your own situation.
You can be determined to have abandoned permanent residence status is you do not maintain sufficiently strong ties to the U.S. Time spend abroad is one type of evidence of lack of strong ties here.
Generally, six months or less spent abroad without reentering is rarely questioned. But once you have spent more than six months out of the U.S., upon reentry they look at several factors to make a determination about your intent to abandon permanent residence - not only the length of time spent abroad but also your family remaining here, property remaining here (especially a home here to return to), a job to return to here, etc.
If you spend a year or more abroad without returning, there is a presumption the you intended to abandon your permanent residence. This can be overcome, but before leaving it would be wise to apply for a "reentry permit" - essentially - advance permission to leave for longer than a year without abandoning permanent residence.
Given your unique circumstances, you should speak to an attorney about the best way to handle this.