It depends on the level of complexity of what you consider to be a 'trait' to begin with. If it's something like "flight", and a species goes 100.000 years without opportunity to use their ability to fly, then the chances of them still retaining their ability to fly after all that time is astronomically small. Simply due to the dependencies such a complex trait would require.

If, by 'trait', you mean something much more basic, like the presence of a particular protein, then that could obviously stick around much longer without active selection.

Destined is the right word, though. Given enough time things will go away without something to keep it in place.