ZAB Controller described an airspace incursion event when failing to note the the automatic hand off feature had not activated.

Narrative

Aircraft X was east-north-east bound at FL390. The aircraft's flight path would almost run parallel to my sectors southern most boundary. The aircraft did cross into my sector by about a 2 miles. I had the hand off and was talking to the aircraft. The next sector along the route has a portion of the sector boundary that bends northward. Ultimately; as the aircraft approaches the next sector (SCT 97); the aircraft needs to be handed off a little sooner; due to the fact that the aircraft gets closer to the boundary sooner. At the time of the event; I do not recall the auto-hand off to be inhibited. In checking the FALCON; this was confirmed; however; I'm not sure if FALCON shows the auto-hand off inhibit. I realized the situation; and called SCT 97 with a late hand off immediately upon recognition. The aircraft was about 1.5 miles from the boundary (still in my airspace) before the hand off and the call for the hand off was made. Being within the protected airspace of SCT 97; I am not sure why it did not auto-hand off. Recommendation; I will pay closer attention to this routing next time. Double check to make sure that the auto-hand off still works; even when almost paralleling the boundary.