The ESA laws DON’T specify a time after which an absence becomes an abandonment. In fact, they don’t discuss abandonment at all, not in BC nor in any other jurisdiction I’m aware of.
Abandonment is actually a so called “common law” rule that comes not from statute but court rulings in which one case serves as precedent for future cases. Although each case is different, it is usually measured in terms of weeks or months.
Also keep in mind that abandonment is based not just on length of absence but other factors including whether the employer takes “reasonable steps” to reach the employee and find out if he/she intends to return. If you can’t reach the employee, you need to keep trying on the general understanding that the more time that passes and the more attempts you make, the stronger your case for abandonment.
Last but not least, it’s also CRUCIAL that you maintain records documenting your attempts to contact the employee.