A very long time. Mine has gone for about 6 months at a time before without eating. Just make sure that there is a source of water in the enclosure for it to drink from and the T should be fine. Just keep an eye open for any major abdominal shrinkage.
My old female only seems to eat well for the first 2-3 months following a molt. The rest of the time, she eats little or nothing. Considering the fact she somtimes skips molting for a year, her fasts can be quite long!