JMdict:
- 不甲斐{ふがい}ない: disappointing; weak-minded; spiritless; cowardly; worthless; pusillanimous; feckless; faint-hearted; shiftless; tame; timid
- 甲斐{かい}: effect; result; worth; use; avail
The word 不甲斐ない has both 不 and ない around 甲斐, and to my understanding the prefix 不- is used to negate words, just like ない. By this logic, the meaning of the word should be "not-worthless" instead of anything negative.
Of course language doesn't work that simply and there must be even bigger "illogicalities" out there that I've just gotten used to, but maybe there is a reason for this one.
Edit: there is also the word [甲斐無い]{かいない} (worthless; pointless; useless) as pointed out by @naruto in comments. Seems like this one works as I would expect.