how long before you loose guild due to inactivity

As per the help article here

Inactive guild leaders
If your Guild Leader has not logged in to Star Wars: The Old Republic on their Guild Leader character for an extended period of time (4 weeks or more), the system will automatically remove them as Guild Leader and pass their leadership on to the highest ranking member who is a subscriber and has logged in within four weeks. If there were no active subscribers in the guild over the last four weeks, the highest ranking Preferred or Free-to-Play member who logged in within four weeks is promoted.

If the member who is promoted to Guild Leader does not wish to act as leader, they can pass leadership on to another officer using the /gabdicatecommand.

If for some reason or another guild leadership isn't passed to someone else after 4 weeks, I would submit an in-game ticket to get the leadership passed.