April to September is not a long time. There's likely nothing wrong. Just keep the plant happy -- plenty of light, water as needed, and enough fertilizer to keep it green. It will likely flower on the next growth flush. 'Tahiti' lime (a.k.a. "Persian") can flower several times a year, usually on the ends of each new growth flush. Has your tree been producing new branches?

Thanx. Yes, it has put out new branches. I'll keep it as long as it's alive, it's still a pretty tree. I hope it'll do something soon, though!

Daes, give the plant time, it'll eventually fruit..some citrus take longer than others..For instance, my Kumquat, Meyers and Ponderosa bloom/fruit more often than limes..
As long as your tree is getting proper care, it will bloom/fruit.
Follow Malcolm's advice..Toni