How long can investors stay outside the UAE? In...

The general rule is that if expatriate residents, that is, people who hold a UAE residence visa, live outside UAE for more than six months continuously, their residency visa will be automatically nullified. If this happens, they will have to apply for a new entry permit to enter the UAE again. 
However, there are some exceptions to the rule, which allow the resident expatriate to stay outside the UAE for more than six months and at the same time maintain the validity of his residence visa. They include:
foreigner wife of an Emirati citizen who is on the sponsorship of her husband
expatriate government employees sent abroad for treatment, provided they submit a medical report approved by Ministry of Health and Prevention or other medical authorities in the UAE.
domestic helpers accompanying Emiratis for studies or medical treatment
domestic helpers accompanying members of diplomatic and consular missions representing the UAE abroad and employees of such missions holding residence visas in the UAE
expatriate residents working for the public sector sent by their employers to attend training or specialist courses, or those working in their employers' offices abroad and their families who are holders of valid residence visas in the UAE
expatriate students studying in universities or institutes abroad (as per Dubai rules). Check with the GDRFA if this applies to your emirate of residence.